omenti

the beauty of two triangles

This morning I overheard a few people fuming about the price of gasoline.  I wonder if they have considered how inefficient their cars really are?

 

The chemical bonds in hydrocarbons are a great way to store energy.  Millions of years ago green plants used the energy in sunlight to split water into hydrogen and oxygen.  The hydrogen was then combined with carbon dioxide from the air forming glucose molecules and giving off a byproduct called oxygen that we've managed to use in other ways.¹  The neat thing is when you burn the glucose,  energy stored in its chemical bonds is released along with water and carbon dioxide.  Glucose is essentially a energy storage battery.  Plants turn it into other hydrocarbon-based substances largely leaving intact the chemical bonds that contain the stored solar energy.  They tap some of the energy for their own purposes and animals eat the plants harvesting the stored solar energy through metabolism - another form of oxidation - releasing the same energy and byproducts as burning.

 

It is wonderful to realize you are really solar powered.

 

Most of the solar energy that powers our bodies fell on the Earth recently - usually within the past year.   It turns out plants aren't terribly efficient - usually less than one percent for those directly in our food chain - but a lot of land is devoted to the cultivation of suitable plants.² 

 

We can have some fun with some numbers.  An average person requires about 2,000 Calories a day.  Calories are a unit of energy so you can divide by time to find the average power requirement.  Doing this and converting to watts, it turns out we need about 100 watts on average.  Lower at night when we're sleeping and much higher when we're doing something athletic, but 100 watts a person is a nice number to remember for quick mental calculations.

 

The sun delivers an average of a bit more than 1,360 watts per meter² to the Earth.³ Absorption in the atmosphere, the Earth's roughy spherical shape, inclination, day and night and cloud cover reduces this to something usually between 50 and 200 watts/m² - let's pick 100 for a quick back of the envelope.  Average food crops stores solar energy into those chemical bonds with at about a half percent efficiency so their power rating is about 0.5 watts/m².  If we could harvest and process these crops with perfect efficiency it would take about 200 square meters of land to supply one of us with food.  Given seasonal growing issues and various inefficiencies in the chain, a more reasonable number is closer to 1,000 square meters of farmland under cultuivation for every person on the planet.⁴

 

So what does this have to do with the beauty of triangles?

 

Hang on - we're getting there.  This is taking a bit more time to flesh out than I thought so I'm breaking my one hour rule.

 

The Industrial Revolution came in several phases, but at its core it allowed us to effectivvely tap the relatively vast amounts of energy stored in hydrocarbons like coal, petroleum and natural gas.  Up until that time most of what we could do was limited to muscle power - from us or domestic animals.  A good rule of thumb is an adult male in good physical shape can produce about a kilowatt-hour of mechanical work a day ..  100 watts of additional power in a ten hour shift.⁵  A horse may provide about four or five times as much.  This proved to be a very low and limiting barrier to growing the civilizations - many people spend all of their time dealing only with food production and available energy for other activities was very limited. 

 

Coal, petroleum, and natural gas formed over many tens of thousands of years millions of years ago.  The efficiency of their formation was not great and local geologic conditions dictated where they are and how much exists.  But many tens of thousands of years often dominates the low efficiencies and large amounts of energy were stored.  We are mining sunlight from our distant past.

 

Most of the gasoline in our cars comes from petroleum which, in turn comes from dead algae and zooplankton that became trapped under sedimentary rock and "cooked" under great pressure and heat for ages.  At about 36 kilowatt-hours per gallon it is almost an ideal fuel for transportation, it can be stored at room temperature, is relatively safe and easy to handle and transport, and we have had engines that burn it directly since the late 19^th century.⁶

 

The ease and low cost of mining, transporting, processing and using this very old reservoir of stored solar energy has produced an extremely inefficient transportation infrastructure - the automobile.  But early on there was so much oil that inefficiency didn't matter very much.

 

Cars are great for moving us long distances at speeds that give us practical commuting ranges on the order of fifty miles or thereabouts and one day trips ten times that distance.  But internal combustion engines are heat engines and, despite more than one and a half centuries of refinement, only about a quarter of the gasoline you buy is used to turn the wheels of your car.  The majority of it escapes out the tail pipe or heats the engine block.  Improvements have been made and will continue, but they are increasingly expensive and we aren't that far from the limits for a flexible use vehicle.

 

There are other issues like cost and pollution, but let's focus on efficiency and ask a fundamental question.

 

What are we really moving?

Usually just a person or two and perhaps a few bags of groceries - a few hundred pounds at most.  The average car weighs nearly 4,000 pounds.  It takes a lot of energy to accelerate its mass to speed, so a good metric to consider is payload divided by vehicle weight plus payload.  Let's say you and your groceries weigh 200 pounds and your car weighs 3,800 pounds.  Only five percent of what is moving around really needs to be moved around.

 

For short trips bicycles make sense.  I've done some calculations based on Colleen and her bike.  She weighs about 170 pounds and her bike weighs 30 pounds.  Fully 85% of what is moving around is useful payload and that number can increase a bit as she carries groceries on the bike.  She gets the equivalent of 1,000 miles per gallon of gasoline.  Her bike is great for speeds up to about 15 mph and trips generally under a five or six miles each way - basically almost any commute in a town or city.  Much longer trips and/or higher speeds or heavy payloads require something like a car - but for short and slow trips Colleen "wins" using a bike largely by not having to carry around all of that extra weight.  We can and should reduce the weight of cars as it is the next area for large (factor of two) improvements in fuel use efficiency, but bicycles are extremely low hanging fruit where practical.

 

In the late eighteen hundreds the biycle, like the automobile, was undergoing change.  The safety bike was developed revolutionizing bike design and safety and giving us a very simple and extremely strong lightweight  structure. It roughly onsists of two triangles fused together.  Bicycle design has progressed, but this basic geometry hasn't changed very much since then.

 

A person on a bike is very efficient - about three or four times as efficient as a walker and more efficient than mamalian locomotion.  Bikes are optimized for urban scale trips and payloads associated with perhaps 80%+ of human trips less than five miles.

 

I sometimes characterize a bicycle as "a human sweat amplifier fashioned of a diamond shaped geometry fashioned from a pair of fused triangles"...  But there is something deeper to it.   Building one can be straightforward - if you like you can even make one using bamboo as a primary frame material.⁷ 

 

Refinements, on the other hand, can be technically demanding and leading edge bike design is a convenient laboratory to material development and fabrication research and development.  The aerospace industryhas been an early driver of carbon fiber use, but bicycle frames have been proven an important vehicle for perfecting less expensive fabrication technologies that are now being applied in a variety of industries.  

 

China has used bicycle manufacture as a mechanism for learning and scaling manufacturing technologies. Beginning with aluminum bike frames in the late 1980sthey have managed to drop the price of an aluminum bike frame by nearly a factor of fifteen.  For about a decade they have been working with carbon filber nad mahve made prie reductions on the order of five with eight or ten looking likely soon.   The resulting techniques have driven wind turbine carbon fiber fabrication along with parts of their aerospace industry.  If they can achieve success in automotive carbon fiber on the order of what they've done with bicycles, the carbon fiber automobile becomes practical and we have a fundamental revolution in the industry.  It would be possible to make a 2,000 pound safe four passenger car and that would translate into much greater fuel efficiency.

 

But bikes may be another subtle, but potentially powerful driver of change.

 

It turns out there are a lot of electric bikes in China - currently 150 million with an annual production that should reach about 70 million around 2015.  Most of these are very unsophisticated - a heavy bike with a small fairly inefficient electric motor and heavy lead acid battery.  

 

Bike batteries don't have to be large and expensive.  We found that Colleen required about 31 Calories to travel a mile making her about 34 times as energy efficient as a 30 mpg car.  31 nutritional Calories is about 36 watt-hours, so a 10 mile roundtrip commute requires about 360 watt-hours.  But Colleen happens to be human and her efficiency at turning food energy into mechanical work at the pedal is about 20% while the battery, controller and motor in state of the art ebike exceeds 80%.  So she could get a comfortable 40 mile range with a 500 watt-hour battery and pedal along a bit to increase the range even more as well as getting some exercise while she's at it.

 

A 500 watt-hour battery pack is about ten times the capacity of the average laptop computer battery.  Currently most lithum-ion ebikes use several laptop batteries, but newer designs use repurposed automotive batteries.  China appears to be encouraging ebike makers to move to lithium-ion designs.  Seventy million lithium-ion ebikes would require 35 million kilowatt-hours worth of batteries.  Smaller electric vehicles use batteries in the 25 to 35 kilowatt-hour range.  eBike production would be equivalent to about a million new electric cars a year and may be an important bridge towards the massive production scales required.

 

There is also an indication that city planners are beginning to rethink the design of new megacities moving more towards a mixture of small cars (mostly electric), ebikes, bicycles, pedestrian traffic and mass transit - much like parts of Northern Europe.  This type of design is much more efficient in energy use and may be less expensive in the long run.   

 

Just two triangles joined into a diamond, but they may be giving us a hint of a possible future.

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¹ Atmospheric oxygen tends to react with a lot of things and doesn't stay around very long on its own - a few thousand years at most.  Its presence indicates something has produced it recently and, at least on Earth, it is an indicator that photosynthesis is working away.

² Sadly there is starvation, but this is a distribution problem.  Green plants provide enough energy for the world's population - but we appear to be within about a factor of two of a fairly harsh limit.

³ 1,366 watts/m² is an accepted number that averages over our orbit and solar cycles, but the last cycle has been very quiet and the recent number is somewhat lower - perhaps about 1,361.  

⁴ This is for diets where we consume plants.  It turns out we eat meat too and making meat is inefficient.  Usually under ten percent, although some meats like industrial poultry can be as high as twenty percent.

⁵ I use a rowing machine to exercise and measure my output directly.  My normal sessions are at an average power level of 150 watts and run 60 to 80 minutes.  A one hour session would represent 150 watt-hours of work.  Since I'm about 20% efficient, that means I need about 600 watt-hours of food above and beyond my normal metabolic needs to support the exercise. That's about 516 Calories (nutritional - there are several types of calories).  People can work at much more intense levels for short periods and expert athletes can work at about three times my level for similar periods.  I note some of that in another post.

⁶ Unfortunately there are some nasty byproducts and side effects.  Incomplete combustion produces numerous toxic chemicals and an enormous amount of carbon dioxide is released as a direct combustion byproduct even if we had complete combustion - approximately 20 pounds of carbon dioxide for every gallon of gasoline burned. This is from carbon that had been captured for thousands of years and sequestered for millions of years. This rapid desequestration is a  root cause of the human caused global warming.

⁷ Bicycle frames are usually fabricated from aluminum, but steel is also frequently used along with the emergence of carbon fiber and, more rarely, titanium.   I'm a big fan of steel as newer alloys are fairly lightweight while offering an outstanding "road feel" Steel can also be easily adapted to bespoke designs where a frame is custom tailored to the rider.  My old Raleigh Pro was built in the mid 1970s using Reynolds 531 - a then exotic alloy that only one company in the world could make.  One of the most exotic steels is a maraging stainless steel called Reynolds 953.  The tube wall thicknesses are so thin - down to about 0.3 mm -  that frames approach the weight of carbon fiber bikes. Colleen is over 6'6" tall and that dictated an unusal frame geometry that required Reynolds 953 and some careful selection of tube diameters, wall thicknesses and buttings to get it "right" ... a fair amount of numerical simulation.

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Recipe   Not re-frieds

I tend to approach cooking on hunches and have my share of failures.  This is a nice success.  I like re-fries, but rather than sautèing the aromatics with the cooked beans I wanted to sautè them first and then cook them with the beans in a pressure cooker to infuse the flavor. I used a mixture of pinto and cranberry beans because that's all I had at the time.  I assume you could use any similar bean and get great results.   A huge key to success with dried beans is to never use anything more than about six months old.

The quantities are approximate as I didn't carefully measure.  I'll use mostly volume measurements even though that is bad form.

Ingredients

° 1 tbl vegetable oil

° 1 medium onion chopped

° 1 bunch cilantro stems and leaves separated and chopped

° 1/2 tsp chipotle powder - use more or less for to vary the flavor

° 1/2 tsp cumin

° 2 cups dried beans.  I used a mixture of pinto and cranberry beans soaked overnight in water - borlotti would be great too

° 2 cups water

° 1 tsp kosher salt

 

Technique

° Heat your pressure cooker with the top off over medium heat and add the oil. Sautè the onion, cilantro stems and spices (not the salt yet) until the onion starts to soften. Don't let it brown. Add the beans and water.

° Close the lid, crank heat to high and lower heat once you reach full pressure (15 psi setting).  Cook about 10 minutes and move to a cold burner allowing the pressure to drop on its own before opening. 

° Reserve a few of the beans for a garnish, add salt to the rest and mash.  

° Serve garnished with the whole beans, sour cream and the cilantro leaves.

 I prefer whole milk greek yogurt (Fage Total) to sour cream, but your mileage may vary.  Sour cream is the classic.  Also I imagine parsley would be a great substitute for cilantro, but I really like cilantro.

 

 

global efficiency and flexibility through local inefficiencies

My sister Corinne has a great love for horses.  Part of it is the beauty of their motion. There are four natural and distinct gaits.  The walk with its left hind, right hind, right front, left front four beat cadence transitions to a two beat gait called the trot as the horse speeds up.  Now its legs are moving in unison in diagonal pairs. It is a very stable gait and the horse’s head is often very steady.  

 

As the horse speeds up the cantor appears.  Now you hear three beats and a pause and then three beats and a pause as one of the rear legs supports the horse as the other three move forward. 

 

As the horse accelerates a four beat gait emerges.  The horse is still pushing off with a rear foot -  for brief moments it has entirely left the ground and is flying.  The full gallop -  as fast as a horse can move.

 

Galloping is not terribly efficient and the horse will tire quickly.  The cantor is more efficient, but not by much.  Walking and trotting, on the other hand, are great paces for a horse if it is to travel long distances.  Horses have very narrow  ranges of optimum speeds.  People can tweak these ranges through breeding altering musculature and leg length, but the horse is a four speed creature with two economy speeds.

 

You might think leg length is an important determinant of the best running speeds in humans, but a look at elite runners - both distance and sprint - show they are mostly of average height.  At six foot five Usain Bolt is a rare exception, but he is the exception in several other metrics.  

 

An examination of the energy used to travel a fixed distance in running is fairly constant over a wide range of speeds - something that is unexpected and very different from horses and other four legged mammals. Adding to the puzzle is the most efficient walking speed.

 

I like to walk and have been on long walks with a variety of people. Most of us are of differing heights, but the average speed we walk at tends to be not that much different from the speed we use when we’re walking along.  Most people walk somewhere between 3.0 and 3.4 miles per hour.  The efficiency of walking is strongly peaked.  If you walk at your own natural cadence you will burn fewer Calories per mile than you would if you were walking at a faster or slower pace.

 

This is very curious as people have very different leg lengths.  At six foot one, but long waisted my 31 inch inseam gives me much shorter legs than six foot seven Colleen’s 40 inch inseam measurement, but her optimal walking speed is only a bit higher than mine and is a small amount lower than another friend who has shorter legs than me.  We give up some efficiency, but it is generally easy for us to adapt our speeds to that of our friends and visa-versa.¹

 

The physics and biology of mammalian location is non-trivial and still under active investigation.  A recent paper that looked into the activity of some skeletal muscles involved in walking and running gives some fascinating insight that paints a picture deeper than the problem at hand.²

 

It turns out it is difficult to directly measure the efficiency of a specific muscle while it is working, but measuring its electrical activity with electromyography is a good proxy and you can estimate efficiency.  Seventeen people were wired up and put on treadmills and asked to move at a variety of paces.  Thirteen muscles were monitored and the muscle activity per distance travel was recorded.

 

 

The results are fascinating.  The plot on the left shows the speed at which a particular muscle was most efficient with walking in black and running in grey.  The plot on the right shows the speed of peak efficiency for each subject for walking and running.

 

Note that the muscle efficiencies don’t peak at the same walking speed - there is quite a bit of variation, particularly in running.  Individually our leg skeletal muscles are not optimally efficient at a single speed. 

 

You might think this is some sort of evolutionary failure, but it is probably the opposite.  We don’t spend our time walking at the same speed even though we do have an optimal walking speed.  We have the need for doing many other activities.  We climb, dance, kick, sprint and have the need to match speeds of others.  These different activities involve each of the muscles in different degrees.  We don’t have the best possible efficiency at our optimal walking speed, but we have a huge amount of flexibility and we have a very wide range of running speeds at ok efficiencies.  Often we are more efficient than the horse - my niece Magi participated in a man vs horse race and dropped all of the horses. 

 

This illustrates something deep.

 

The best general purpose optimization often involves a mixture of non-optimized components.  Making each component as good as it can be by itself and allowing it to operate where it runs best usually results in a larger system that is far from optimal.  This is central to engineering which is the practice of finding and harmonizing a variety of pieces into a whole which is the best compromise.³

 

 

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¹ How people communicate the proper walking speed is a fascinating look into the subtle non-verbal ways we communicate with others.

 Note if you are walking for exercise and walk over a fixed distance slowing down or speeding up from your normal pace will burn more energy. Speeding up burns the most and if you are walking for a fixed amount of time - say and hour - the higher speed will usually burn the most energy.  

The relationship between efficiency, performance and physical size is a rich subject area and sport is an excellent lens to illuminate interesting questions.

 

² The musculoskeletal system of humans is not tuned to maximize the economy of locomotion

David R. Carrier, Christoph Anders, and Nadja Shilling

Abstract

Humans are known to have energetically optimal walking and running speeds at which the cost to travel a given distance is minimized. We hypothesized that “optimal” walking and running speeds would also exist at the level of individual locomotor muscles. Additionally, because humans are 60–70% more economical when they walk than when they run, we predicted that the different muscles would exhibit a greater degree of tuning to the energetically optimal speed during walking than during running. To test these hypotheses, we used electromyography to measure the activity of 13 muscles of the back and legs over a range of walking and running speeds in human subjects and calculated the cumulative activity required from each muscle to traverse a kilometer. We found that activity of each of these muscles was minimized at specific walking and running speeds but the different muscles were not tuned to a particular speed in either gait. Although humans are clearly highly specialized for terrestrial locomotion compared with other great apes, the results of this study indicate that our locomotor muscles are not tuned to specific walking or running speeds and, therefore, do not maximize the economy of locomotion. This pattern may have evolved in response to selection to broaden the range of sustainable running speeds, to improve performance in motor behaviors not related to endurance locomotion, or in response to selection for both.

 

 

³ A week or so ago I was in an email conversion where someone noted a Steve Job’s quote and I reacted.  I think Apple is an excellent example of a company that understands not only how to make these engineering compromises, but also that the final product involves more compromises than are possible if you “just” use the discipline of engineering.  Consumer electronics has evolved beyond engineering.

 

[friend quoting Jobs} “When you first start off trying to solve a problem, the first solutions you come up with are very complex, and most people stop there. But if you keep going, and live with the problem and peel more layers of the onion off, you can often times arrive at some very elegant and simple solutions. Most people just don’t put in the time or energy to get there. We believe that customers are smart, and want objects which are well thought through.” - Steve Jobs

 

[me] Absolutely - and this is *so* different from ordinary engineering and product development. 

 

[friend] How so?

 

[me] This is a *very* long subject so I'll try to just hit a few points.  Engineering is all about finding a compromise among various components to create something that makes specifications.  Great engineers are really good at this and I have enormous respect.  The key point is there is an end point - after all, something has to ship on a certain schedule.  When you are doing this you can only work within a fixed domain.  It can happen that you bump into something new as you work on something, but that is rare and certainly not your job description.  In recent years the goals of a product are specifications and hitting price targets.

 Apple certainly does engineering, but it is a different scale.  Other non-engineering disciplines are involved.  During the design phase there is this tendency to keep going deeper.  Occam's razor is a fundamental driving principal.  You need to simplify wherever possible *even* if you didn't think it was possible at first.  There is also a sense of artistic elegance and pride that comes into the optimization.

All of these competing subcomponents and pieces of software have qualities of their own - along with time dependent evolution curves.  You need to be suboptimal on several to make the global result better.   Much of conventional engineering ignores the fact that real consumers also like to see elegance and a simple UX mixed in too … in fact those may be the defining characteristics of a product.  And the product needs to dance properly with other products in addition to the person who uses it.  Getting these details right is an entirely different skill set and Apple has built an organization that understands this deeply.  Artists get it deeply. 

 Jobs once described himself not as a technologist, but rather as an artist who paints with technologies.    

My heritage and way of looking at the world is through the perspective of science.  Here you are trying to figure out how nature works.  There is an absolute you are working towards, but she tends to reveal herself only when questioned properly and then only a bit at a time as you need to find better questions to progress.  I was not attracted to biology or chemistry as they are so complex.  (they are still very beautiful - but it is a preference of mine)  I found physics to be my sport as it is so simple - you only look at the most simple systems, but you want to go in as deeply as possible. The idea is to find the really fundamental questions.  I find the people who have sensibilities most similar to mine are artists and composers.  

Apple is the company with these sensibilities as they are trying to peel the onion back as they progress.  The analogy isn't great - they are probably closer  to biology as they are working in a complex environment -- Jobs, in a different time and if he would have had academic leanings - may have made a great biologist.

As these products that combine art, electronics and computation progress conventional engineering is going to be an increasing failure as a global solution.  It is a piece of what needs to be done, but the integration with other disciplines is central and, I think, a requirement for success in at least the consumer product environment.   There are so many things that need this approach.  It is terrifically exciting. 

 

electric car 101

A question came up yesterday about electric cars and it is clear there is a lot of confusion about some of the fundamentals.  Here is a one minute primer.

 

First you need to think about the difference between power and energy.  It isn't technically an accurate definition but think of energy as a storage system that you can draw on to move things. You may choose to use it quickly or slowly.  The rate at which it is used is power.

 

Think of energy as gasoline and power as what you control with the accelerator.

 

There are any number of labels to measure energy and power and this serves to confuse people.  Energy is just energy and power is just power, so the trick is to pick a unit that is appropriate for the task.  For the automotive world kilowatts (kW) is a good choice for power and kilowatt hours (kWh) for energy.  Remember that power is the rate of energy "used" in a given time so this make sense kWh/h = kW.¹

 

A gallon of gasoline represents about 36.6 kWh of chemical energy that can be liberated when it is burned.  You can put this into a lawn mower and run it for hours or a Ferrari and use it in a few minutes if you can find a road that can handle 200 mph.

 

The battery in a Chevy Volt can store about 16 kWh of electrical energy.  Batteries are large, heavy and expensive compared to the equivalent amount of energy.  So the Volt stores about the same amount of energy as a half gallon of gasoline. A Nissan Leaf stores the equivalent of three quarters of a gallon and the Tesla Roadster about one and a half gallons.

 

It may seem like a lost cause, but the energy must be turned into motion.  An electric car does that with about an 80% efficiency and a gasoline car about 20% - the electric car will go four times as far on an equivalent amount of energy.  And if you compare either with muscle power it quickly becomes apparent why the Industrial Revolution was so significant.

 

So the Volt has about the range that two gallons of gasoline will give in an equivalent sized car and the Tesla has a seven gallon equivalent.²

 

The energy storage numbers may seem small, but they are in the ballpark for commuting.  This is the first time batteries have been good enough to be useful in a 3,500 pound car.  You could make them much more useful by lowering the weight of the car and/or increasing the amount of energy that can be stored in the battery.

 

As for power the battery pack on the Volt can easily delivery energy at a rate to produce up to 111 kW in the car's electric motor - this works out to 149 horsepower.  The Tesla is rated at about 215 kW, which is 288 horsepower.  Automotive scale battery packs that can deliver much more power can be assembled, but the car's range is very low at those rates.  But the bottom line is conventional lithium-ion battery packs can supply enough power to provide gasoline car-like accelerations and cruising speeds.

 

Sorting out the economics is another issue.  10 kWh of electricity is sufficient for 40 miles of driving in a Volt.  At average American utility rates that costs about $1.30 (perhaps under $1.00 if delivered off-peak).  That same 40 miles might require $5 of gasoline in a similar class vehicle.  

 

Of course there is this little matter of battery cost...

 

A Volt battery pack may cost as much as $10,000.  It has some specialized electronics along with the battery and a shielded crash proof casing.   This compares to about $1,000 for the gas tank and fuel handling components of a conventional gasoline powered car. Pure electric cars like the Leaf have lower power train costs and are likely to have much lower maintenance costs over the life of the vehicle.  

 

Currently it is difficult to justify a pure electric car without the $7,500 (or more) subsidy that partly bridges the cost of the energy storage component of the vehicle.  If cars weighed half as much as they do the break-even point would be much closer.  But there is that nagging issue of range.

 

The Department of energy has a variety of programs aimed at doubling the amount of energy that can be stored in a kilogram of a production battery by 2020.   Other goals would reduce the price of a Volt scale pack to under $2,000 by the end of this decade -something that appears to be feasible. An exotic type of battery, a rechargeable metal air battery, could conceivably improve this energy density by a factor of twenty. 

 

Ultimately electrics win as the factor of four in efficiency is too great and battery costs will fall and, with the right upstream energy source, electrics can be very clean.  My best guess is subcompacts will be at parity in price around 2020.  Driving range will not be at parity though.  You will be able to buy 300 mile range pure electrics, but there will be a penalty in purchase price.

 

Real change may occur late in North America.  The real game for the car makers is the "megacity car" - small low range vehicles for the emerging middle class in China, India and other very high growth areas.  The economics of smaller cars may make electric power trains likely in massive scales in the next decade or two.

 

In the meantime there is much you can do in the present to dramatically increase your effective travel efficiency - make your driving more efficient and eliminate it where possible.  

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¹ In working through physics problems it is convenient to do a quick check to make sure you have the units right.  If you don't there is an error - it would be nice if the media understood this.  Major pieces appearing in the papers and on TV often fail.

² Although the battery can store 16 kWh, only 10.4 kWh is tapped to allow the battery pack to have a long life.  So the useful equivalent is about 0.3 gallons of gasoline and the range is about the same as 1.2 gallons when you factor in the improved efficiency of the electric drive train.

two triplets of choice and truly massive change

Recently I entered a conversation with an organization that is working on a better understanding of how people might respond to global warming and what are the elements that can impact our choices for change.

 

The subject is enormously complex and multi-disciplinary.  In some parts of the world, notably the US, it has also become politically charged.  But human caused global warming clearly exists and there will be increasing impacts.  That makes it a fantastic problem - perhaps the most important change problem over the next few generations.

 

I like to think about our response to it in terms of admixtures of choices that come in triplets.  The first triplet is how we deal with it.  The choices are mitigation, adaptation and suffering.  Most analyses show mitigation - reducing the impact of the change by working on decreasing its scale before it becomes severe - to be far and away the most cost effective choice.  The costs are still viewed as high relative to other societal costs and most people don’t see the threat as immediate and severe enough to warrant serious efforts.  

 

But even if we could do something dramatic there is something of a flywheel effect from greenhouse gases in the atmosphere.  We will see an increase in average temperature even if we were to cut our emissions to nearly zero and we’ll have to deal with the consequences as nature adapts - after all, many of us and our children will be around for the ride.  We can control the amount of adaptation either through mitigation or by simply ignoring mitigation and adaptation.  

 

Doing nothing will result in increased human suffering.  The uneven distribution of wealth and resources to people will create pockets of losers and these may be enormous.  A few years ago I spent some time in a group thinking about some of these issues and was left deeply troubled - the sort of thing that wakes you up in the middle of the night with awful nightmares.  Some of these it is probably taking place now, although currently one can only look at these events statistically.  

 

The average world temperature is increasing and that is beginning to have a measurable impact.  Most of us think in terms of sea level and shrinking ice caps, but changing climates are probably a larger issue.  The Earth has seen higher and lower temperatures, but these changes generally have occurred over time scales that have allowed evolution to adapt.  The current changes we are seeing are taking place at a time scale that is much faster than the capacity of evolution to respond.¹

 

Most of our energy comes from the burning of fossil fuels - essentially carbon that has been stored over millions of years.  Traditionally there is a balance in the carbon cycle with the amount of carbon dioxide in the atmosphere being more or less regulated at about 275 parts per million (ppm) in recent times.  At least until the beginning of the Industrial Revolution.  Now we could burn coal, petroleum, and natural gas.  All of these were formed by storing carbon that was fixed in photosynthesis over millions of years in a very short amount of time.  Nature is incapable of regulating the increase at the pre-Industrial Revolution level and the amount of carbon dioxide in the atmosphere to creep up to a bit more than 390 ppm  this year.  It should pass 400 ppm by 2015 at the current rate of increase and much larger numbers seem almost certain.  

 

If we were getting most of our energy - say more than 90% -  from non-carbon sources there would be no global warming issue.  We don't, but we have the capacity for change and that brings me to the second triplet. 

 

You can lower the amount of carbon released into the atmosphere by using some admixture of conservation, efficiency, and new types of production.

 

Conservation should be a no-brainer, but convincing people to change their usage patterns can be difficult.  Conservation seems to require motivation, a perceived ability to do something and a trigger that prompts action.  Putting this together rarely happens automatically.

 

At a personal level we were able to decrease the amount of gasoline burned in our car from about 650 gallons per year ten years ago to around 200 gallons per year now.  A bit over 20% of that was from improved efficiency in my driving technique and tweaks to the car itself, but most of the reduction came from simple conservation - careful trip planning and the elimination of unnecessary driving.  The steps are simple, but cars are so convenient that it is difficult getting people to make the efficiency or conservation choice.  For many of us efficiency seems to only be considered when a car is traded. 

 

President Carter famously ran into political problems when he suggested people conserve energy at home and even more when a 55 mph speed limit was introduced (although one can argue that is an efficiency step).  Since then politicians seem to work under the assumption that the American voter is lazy and incapable of serious sacrifice even if sacrifice now may lead to a better future.   They seem to believe we are only capable of responding to the immediate.

 

Efficiency is interesting as more efficient devices can those that use more energy and the user is not left with the conscious decision that conservation requires.  An unsung hero of the efficiency game is Art Rosenfeld of LBL - I strongly recommend a talk he gave a few years ago:

 

 

You do have to be a bit careful implementing efficiency.  A car that is five percent more efficient than what you have may be appealing and it probably makes sense to move to more efficient cars when you trade, but moving just based on efficiency neglects the energy required to build the car in the first place - a figure that is often the equivalent of a year’s worth of driving.  On that basis there may be no energy payback from a small efficiency improvement.  On the other hand there may be enormous opportunities that you are overlooking.

 

Some people suggest that improve efficiency leads to greater energy use and imply that it doesn’t make sense to make our energy using devices more efficient.  The Jervons Paradox is usually invoked in their arguments. In 1865 William Jervons published The Coal Question which argued that producing goods with less energy would not result in an energy savings, but rather would encourage so many new goods that ultimately more energy would be used.   The paradox is also called rebound and, where increased consumption trumps the savings from efficiency, backfire.

 

In the December 20, 2010 edition of The New Yorker David Owen published a popular piece on this under the title “The Efficiency Dilemma”.  Unfortunately his analysis doesn’t hold up under careful examination.  It is the result of careful cherry picking that distorts a larger view of the issues involved.² The net result of smokescreens like this is there is a lot of pushback on the move to increase efficiency even though dramatic improvements have been made since the OPEC embargoes and we are seeing the potential for even more.  There can be an enormous bang for the buck here - but, of course - the payback is not immediate and many organizations are not equipped to perform the analysis required to uncover choices that will help them do more with less.

 

New sources of energy production are sexy for the engineer as well as the investor and ultimately we have to move much of our energy production to low or no carbon sources.³  As new power plants are required it makes sense to move away from high carbon sources, but costs are the driving issue.  Hydrocarbons and the machines that convert their stored energy into more useful forms are very inexpensive - particularly as their economics rarely involve the costs of their carbon emissions.  Working at this level, for small and large scale operations,  often involves government policy as these plants are expensed over very long periods of time.  

 

Most people tend to concentrate on new sources of energy as that appears to require the least change on their part.  You can simply use your stuff and don’t need to change your lifestyle assuming the price changes are sufficiently small.  It is a nice way to avoid thinking about the more complex problem.

 

In summary conservation can be immediate and very inexpensive.  Efficiency improvements take more time and generally have a cost associated with them, but often (not always!) have a greater impact than conservation for the average user.  Moving to new sources of energy is sexy and tends to be expensive (at least over the short term). It offers the least bang for the buck, but it is centrally important over the long term.  All of these can be very inexpensive if applied to mitigation, but people usually neglect the proper analysis of including externalities in their calculations.

 

Going back to the first triplet, mitigation is probably the best and least expensive approach, but the train has left the station and we will be forced to adapt to some change that is inevitable.  How much is an open question and we will have some control over that.  Suffering will also occur - mitigation and adaptation can minimize that, but all of this is expensive, political and off the radar of most of us.

 

The holidays are traditionally a time of hope - after all, the Winter Solstice marks a point where we can now look forward to ever increasing amounts of light.  I don’t mean for this to be a bleak and troubling piece, but rather note we are still at a point where we have choices and much can be done.  The difference one person can make is not necessarily insignificant - look at what Art managed to do - but even if you only make changes in your own life and that of your family, that is progress.  And maybe you will be rewarded with a different perspective for looking at the world.

 

If you try something that you hope will impact others recognize that it may well fail and learn from it.  I spent about a year working with a friend on her plan to promote gardening and biking among children in Southern California.  The ride was bumpy and the program ultimately failed, but it wasn't terribly expensive and we learned a lot from the experience.  Hopefully enough to make the next effort - or the efforts of others - more positive.  And even a failed project is much more rewarding than watching television. 

 

I’m very excited to be working with this small group as they are very serious about trying to move the needle on changing the attitude of people.  This is something that is required if we are going to minimize suffering of our children, grandchildren, great grandchildren and beyond.⁴

 

_____

 

¹ At least one of the six great extinctions - the Permian-Triassic event - may have taken place in under 1000 years, so there may be a precedent for something as swift as what we are now witnessing. It is important to note that the real issue is not the absolute temperature change, but rather the rate of change - dT/dt, where T is temperature.  As humans 30 to 100 years seems like a long time and is something we generally don’t plan for, but anything under a few thousand years is a twinkling for natural responses.  We have a huge mismatch.

² It is way beyond the scope of a small posting to get deeply into this, but Owen argues that rebound effects are often in the 10 to 30 percent range and can exceed 100%.  In reality they are usually in the small single digits where they exist at all.  Most devices have relatively modest energy costs that few people respond to.  Responding saved energy costs does lead to indirect energy use, but from 1986 to 2006 only about six to eight percent. Furthermore no saved money can buy more than 100% of the energy in that was originally saved (at least not unless you change to a different type of energy with dramatically different costs).  Most people don’t understand the energy costs of their home furnace or air conditioner and don’t use it more because it is cheaper to operate.  Future energy savings are diluted by capital costs and generally heavily discounted.  Owen improperly neglects other contributing factors to economic growth.  His article is intellectually very fuzzy and lacks rigor and proper logic.

³ Production is an inappropriate term that all of us use.  We don’t “produce” energy, but rather convert it from one from to another as physics tells us energy can’t be created or destroyed and is always conserved.  When we burn coal we are turning energy stored in chemical bonds within the coal into thermal energy and this thermal energy generally produces steam that drives a turbine converting thermal energy into mechanical energy.  The turbine spins a generator converting mechanical energy into electrical energy which is a form we can easily distribute and use.  We think of coal as a fundamental energy source as we mine it, but it is really stored solar energy that was captured by plants usually millions of years ago.

⁴ Sukie and I don’t have children.  Many of the scientists I know who study the impact of global warming - particularly the effects on the ecosystem - seem to have lower fertility rates.  I can understand why as there is a great amount of pessimism that suffering can be avoided.  I’m cautiously optimistic, but doubt we’ll do anything close to optimal.  I may not have children, but I do have younger friends I love and what they may have to deal with deeply disturbs me.

__

The drawing is from the extremely skilled pen of Gary Zamchick who created it for Colleen Smith.  Gary is a great guy for involving art in the process of innovation.  I've worked with him and give him two thumbs up:-)

 

dealing with incomplete models - understanding nutritional energy balances

What happens when you are trying to modify your behavior with information that comes from measurements that can be difficult that feed into models that are fundamentally inaccurate even though the you may not suspect the models are flawed?  How do you understand this well enough to get a useful signal in a very noisy environment?

 

For many of us the period between Thanksgiving and the New Year involves way too much food. I’m trying to maintain my weight after a serious ten month diet and this means measuring and tracking what I eat as well as my exercise. 

 

It should be simple - after all, energy is always conserved.  Food is just a way to store energy.  If you eat as much as you require to stay alive, your weight should be stable.  Eat a bit less and/or do a bit more physical work and you should lose weight. Take in more than you need and your body tries to hold onto the extra energy by turning it into a energy stored in you - body fat.

 

But to do this simple calculation requires you have to know how much of the energy in food is accessible to your body, how much energy your body uses to run itself and how much energy it takes for you to do any kind of physical work.  All of these are difficult to know to a good degree of precision.  We have published guidelines, but few of us consider the error bars on the underlying measurements and calculations and some of the pieces are still being discovered by basic research.   

 

We tend to assume food nutrition labels are accurate, but it turns out they are based on a technique that is about one hundred years old.  That system, the Atwater System, has known flaws, but nothing has been found to be easy to use and more accurate.

 

Wilber Olin Atwater was a professor at Wesleyan University and a central figure in understanding modern nutrition.  By the mid 1800s people had worked out that proteins, fats and carbohydrates were major components in human nutrition and estimates were made of how much energy was available from each through metabolism.  

 

Atwater spurred the creation of an American nutrition research enterprise - one of the first examples of government funded big science outside of the military - and calculated how much metabolisable energy was available in proteins, fats and carbohydrates accounting for the efficiencies of digestion.  It became possible to measure the chemical energy in food  components and predict how much we could use.  You could simply measure the amount of protein, fat and carbohydrates in a food and determine how much energy the human body would extract.¹

 

The current standard used in the US and many other countries takes into account a few other nutrition sources and food labels are based on the following conversions:

 

	kJ/g	kcal/g
fats	37	9
proteins	17	4
carbohydrates	17	4
fiber	8	2
ethanol (alcohol)	29	7
organic acids	13	3
polyols	10	2.4

 

It turns out this is only a general approximation and to first order you can get away with just looking at the fats, proteins, carbohydrates and alcohol figures if you are creating your own recipes.

 

But your efficiency at absorbing food varies.  New work that looks at how the food was prepared suggests that food that is mechanically made into smaller bits is more efficiency absorbed and food that is cooked is absorbed even more metabolised.²  The largest effect is cooking.  Muscle proteins, sugars in starches and other energy laden molecules are physically opened up allowing digestive enzymes to attack their amino acid chains more effectively.  Food that is cooked gets more of its energy into your system than food that isn’t.  The science is still developing, but some researchers speculate cooked foods provide at least 10% more energy than raw foods and the number may be higher than 25% - I wouldn't be surprised given some of the preliminary results. 

 

The effect of cooking is not accounted for by nutrition labels.  So if you want to lose a bit of weight you might try increasing the raw food component of your diet.

 

The energy balance for your body has four general components: energy intake from eating, energy expended keeping your body running, energy spend doing physical work, and energy spent in thermogenesis (shivering for example).  Physical work comprises about  20% of the average person's energy budget, thermogenesis is usually under 10%.  Most of the energy we use goes into keeping our bodies functioning - our  Basal Metabolic Rate (BMR).³

 

Once you have an idea what your BMR is you can add up all of the physical activity during a day and have a fair idea what your intake should be - assuming you have a good idea of how much energy your body is getting from food.  This gets tough, so most people who worry about this talk in terms of basic activity levels that range from 1.2 for sedentary office workers to around 2.0 for people with physically active lives.⁴

 

My BMR approximation is 1,583 kcal a day by the basic calculation.  Colleen’s is 1,724, but her real figure is higher as she is very athletic.⁵

 

If you exercise regularly you can calculate the energy spent during exercise and add that to your BMR for a rough approximation - a lower limit as you move around doing other things during the day and there is some thermogenesis.  Unfortunately energy spent during exercise is only an approximation as our efficiencies vary person to person for various exercises.  That said you can probably get 80 to 90% accuracy using tools like this one.⁶

 

If you have made it this far the act of journaling your calories and exercise appear to be a futile effort as there is a huge amount of underlying complexity.  But you can get around that.

 

Keep track of your weight too.  If you plot the results you can get an idea of what your measurements for activity and eating mean assuming the types of food you eat and the activities you do don’t vary dramatically.  The numbers may not match what you would measure in a lab, but getting the bottom up numbers to match the top down results is extremely difficult even in that setting.

 

Absolute numbers are very difficult to measure in this case, but it is possible to come by a stable relative measure, and that is all most of us need for this purpose.

 

My goal was to lose about 5 pounds a month while dieting.  Using the rough figure that a pound of fat (what I wanted to lose) is about 3,500 Calories, I aimed at an average daily deficit of about 625 Calories through a combination of exercise and eating less food.  It worked and I was able to maintain a fairly constant rate until near the end when I wanted to gracefully transition to an exercise/eating routine that might be sustainable.⁷

 

Even though we have flawed models for how much energy we absorb from our food and how efficient our bodies are, the models are sufficient - with a bit of analysis - to effectively use as a tool for losing and maintaing weight.  It is easy to imagine local refinements - I’ve created a tool that helped me understand my own information flow and ultimately how that translates into weight - and it is likely that activity monitors like accelerometers can help, but in the end simple willpower rules.  I suspect many monitoring and computational aids will ultimately fail unless they can impact our basic urges.  To control something you need to combine motivation, the ability to make a change and some triggering event.  I’ve worked that out for myself.  Building a general tool seems difficult.

 

Perhaps what we really need to do is find the levels of eating and activity that evolution assumes.  Up until the Industrial Age people appear to have been self regulating in weight.  Now foods tend to be more plentiful, have greater energy densities and perhaps are even more palatable.  At the same time many of us are less active.  The balance is thrown and many of us gain weight easily.  Finding the right balance is tricky as evolution did not design us for a long and healthy life - basically we get to the point where we have been able to reproduce and then things begin to fall apart.  So the full nutrition offered by earlier diets may be very suspect even if the energy balance is good.  There is probably quite a bit to learn here.  Some of us (not me) are fortunate enough to have bodies that are great at self regulation.  Exactly how that happens is a very interesting question.

 

_________________

 

So now we shift gears and present a few deadly recipes:-)

 

No one seems to be complaining about the recipes and three people have asked for more, so here are two rich desserts - a banana cream pie and a lemon tart.  Both use the same shortbread crust.    

 

I think of baking and cooking as two very different arts and suspect few really outstanding cooks are also outstanding bakers.  Cooking demands knowing the state of the food and how flavors link up - there is a lot of improvisation that occurs as you cook so measurements are just a guide.  Baking, at least for me, demands careful measurements for ingredients and cooking, so I use weights rather than volumes.  I have a great $25 scale that measures accurately to the gram and recommend something like this to anyone who bakes.  I’ll leave the conversions to you if you bake using volumes.  

 

Both of these are very easy, delicious and something you should only eat sparingly.  They were part of Sukie’s birthday present a few days ago.

 

The shortbread pastry crust is really simple and no rolling is required.  Just put a few ingredients into a food processor, pulse a few times, and press into a tart pan.  I do recommend very fresh ingredients for baking.  Sugar or flour that has been opened and sitting around for a month or so pick up a funny taste.

 

Shortbread Pastry Crust

 

130 grams all purpose flour

35 grams powdered sugar

 a pinch of fine sea salt (too small for my scale - I’m guessing about 1/8tsp).  Note that iodized salt picks up a strange flavor when baking, so I use a fine grain un-iodized sea salt

 1 stick of cold unsalted butter - about 115 grams

 

 procedure

 

° heat oven to 425°F with the rack in a center position

° butter or lightly spray with a nonstick neutral vegetable oil cooking spray an 8” tart pan with a removable bottom. 9” would probably work too.

° cut the butter into chunks and put all of the ingredients in a food processor 

° pulse the food processor until the pastry starts to form into pea sized clumps - about 30 seconds for me.  don’t let it grow into larger pieces if you can.

° press the dough into the pan and pat as evenly as you can

° pierce the bottom of the crust with a fork to prevent it from puffing up too much during baking.

° Cover the pastry with plastic wrap and put it in the freezer for 15 minutes - this is a really neat trick that prevents the crust from shrinking when it bakes.

° Bake until the crust is golden brown - about 15 minutes for me.  Cool on a wire rack.  You can cover the crust and store it for a day in the refrigerator f you want. 

 

Lemon Tart

3 large eggs at room temperature

150 grams granulated white sugar

80 grams fresh lemon juice (about 3 lemons)

a half stick of butter - about 56 grams - at room temperature - cut into chunks

4 grams of lemon zest (be careful to only get the yellow part!)  I prefer a microplane for doing this

shortbread pastry

30 grams finely chopped almonds

blueberries and maple syrup - thawed frozen blueberries are fine

 

procedure

° In a double boiler over simmering water whisk the eggs, sugar and lemon juice together

° Cook, whisking or stirring with a spatula, constantly until the mixture becomes pale and thick - about 160°F.  This takes about 10 minutes

° Remove from the heat and strain to remove lumps.  

° Whisk the butter into the mixture until melted and add the lemon zest.

° Cover with a plastic sheet pressed to the surface of the lemon curd to prevent a skin from forming and let it cool to room temperature before filling the crust.

° Assemble covering the inside of the crust with finely chopped almond bits and then pour in the lemon curd.  Even out with the back of a spoon or a pastry knife.

° Separate the pie from the pan - just carefully push from the bottom

° Add maple syrup to the blueberries and spoon on to individual pies of the pie when you serve.  Sweeten as much or as little as you like.  

 

 

Banana Creme Pie

 

300 grams whole milk

half a  vanilla bean (you could use a good vanilla extract - maybe about a half tablespoon)

 3 large egg yolks at room temperature

 50 grams granulated white sugar

 20 grams all purpose flour

 20 grams corn starch

 3 large ripe bananas

 40 grams shredded coconut

 whipped cream (recipe at the bottom)

 

procedure

 

° Score the vanilla bean and add to milk in a saucepan and start heating at a medium heat

 ° While this is cooking mix the sugar and egg yolks together. then sift the cornstarch and flour into the egg/sugar mixture to make a thick paste.  Don’t let this sit around as it gets very lumpy if you do.  

 °Stir the warming milk.  Take it off the heat when it begins to foam and remove the vanilla bean.  Slowly add the hot milk to the paste whisking constantly.  

 ° Scrape out the seeds from the bean and add to the mixture.  If you use vanilla extract instead, now is the time to add it.

 °Pour the mixture back into the saucepan and heat over medium heat until it begins to boil and thicken.  

 ° Pour the mixture into a clean bowl and press plastic wrap to the top surface to prevent a skin from forming.  Let it cool to room temperature.

 ° Slice the bananas and fold two in with the cooked mixture along with the shredded coconut.  Pour into the pasty.

 ° Top with whipped cream and carefully release the pie from the pan side ring

 

 

Whipped Cream

 

120 grams heavy cream chilled

 15 grams powdered sugar

 1/2 tsp almond extract

 

procedure

 

° Chill a mixing bowl and beater from an electric mixer in the freezer for about 5 minutes.  You can also get good results with a whisk and copper mixing bowl, but that takes some elbow grease.

 ° Pour the cream, sugar and almond extract into the bowl and beat until peaks form.  

 

 

____________

¹ Atwater showed about 4 nutritional Calories (kcal) were available from carbohydrates, 4 from proteins and 9 from fat. 

² There has been a lot of speculation here, but now serious science is being done that supports the notion that cooking makes more energy available.  A paper by Rachel Carmody and Richard Wrangham in the Journal of Human Evolution is a good example.  Another study found that cooking gelatinizes starch meaning amylopectin and amylose are released and exposed to enzymes making more energy available.  Cooked starches have more available Calories than those that are raw.

 People have known for a long time that people who eat mostly raw food tend to be very thin compared with the general population, but serious studies on those populations are recent and the results spurred a deeper look into the more general question of food processing and available energy.  Women on a purely raw food diet regularly lack the energy to have a functioning menstrual cycle even though they are eating what should be a high quality diet.  The available Calories just aren’t there - we have based our food recommendations on cooked food and our bodies seem to have a body regulation mechanism that is based on cooked food - this may even be a short term evolutionary response, but that is currently speculation waiting on the verdict of science.

³ BMR is difficult to measure directly as it requires the measurement be made while the person is at rest for a long period.  A more common technique is to measure a person’s resting metabolic rate (RMR).  They turn out to be closely related and similar under most conditions.

A frequently used approximation is from Mifflin et. al. (1990):

BMR = 10*weight + 6.25*height -5*age +s  

where weight is in kilograms, height is in centimeters, age is in years and s is +5 for males and -161 for females.  

If you know your lean body mass in kilograms the Katch-McArdle approximation is probably more accurate.

BMR= 370 + (21.6 * lean body mass)

BMR in both of these approximations is in kcal (nutritional Calories)

⁴ One approximation is the Harris Benedict formula:  

sedentary office workers use BMR *1.2 Calories

light exercise 1-3 days a week use BMR * 1.375 Calories

moderate exercise 3-5 days a week use BMR * 1.55 Calories

hard exercise 6-7 days a week use BMR * 1.725 Calories

very hard physical labor use BMR * 2.0 Calories

This is very approximate.  Athletes in training can use incredible amounts.  Colleen was in the 5,000 to 6,000 Calorie a day range when training - easily blowing through the approximation for very hard physical labor.

⁵ Normally men have higher BMRs than women even when they are the same height and weight. Men, on average, tend to have a higher percentage of lean muscle.  Colleen is a bit heavier than me and, at 200 cm, quite a bit taller. She is also younger - all of this is enough to give her a higher BMR.  Since she is thin and athletic you really need to use a different approximation as her body fat is low at around 10%.  The Katch-McArdle formula gives a better BMR estimate of 1,925 kcal

Some unit notes:  Energy is just energy.  kilocalories (kcal) are the same as nutritional calories (Calories).  Converting 1,925 Calories to watt-hours we see Colleen’s BMR is about 2,239 watt-hours a day.  You can divide this by time to get her average power expenditure from BMR -- a bit over 93 watts.

In an inactive office worker mode she would need about 1.2 * BMR or 2,310 Calories a day - a figure that would cause a smaller person, even someone who is fairly active, to gain weight.  Of course a very heavy person would have a very high BMR and their weight loss in pounds per month can be very high.

⁶ Note that this is energy used above and beyond your BMR.  Often people assume the exercise figures are a person's total requirements during the exercise period.

⁷ I strongly recommend a good piece of software for logging exercise and meals.

Now I can deduce my daily requirements to be about 2,190 Calories per day.  This is consistent with my calculated BMR times a factor of about 1.4 for my normal daily activity.  It sort of makes sense.

 

seven billion

It is impossible to know how many people are currently alive, but the best estimate suggests today the figure passes seven billion people.  One worries about what the world will look like in 2050 or 2100.    Some argue, as they do with energy, that some magic bullet will be found - after all, mechanized farming and two green revolutions allowed us to move from one to seven billion people.  Unfortunately past revolutions are no guarantee new and sufficiently good revolutions will appear.  There is also the sad fact that the world currently does not support seven billion people without hunger - as currently about a billion people are malnourished and few of us seem to worry very much.

 

I spend a lot of time thinking about energy and its flow through society.  One of the larger components is associated with food and it is clear we are up against several severe limits - available farmland, water and climate change to name a few.  One can imagine several back of the envelope changes that would make enormous differences, but how practical are they and how do they interact with other pieces of the puzzle?

 

Several communities are focused on the problem.  One of the more articulate researchers who has been looking at possible paths that don't require the invocation of miracles is Jonathan Foley of the University of Minnesota.  Check out his TED talk

 

He has a piece in the November, 2011 Scientific American on feeding the planet that explores the subject a bit more deeply focusing on miracle-free steps that could ensure enough food production to nourish the likely 2050 population.  I strongly recommend reading it.  (the magazine is currently on the newsstands and in most libraries - the digital copy is here).  For those of you with a scientific background I strongly recommend a piece that appeared a few weeks ago in Nature:

 

Solutions for a cultivated planet

Jonathan Foley et al.

 Nature 478, 337–342  (20 October 2011

  doi:10.1038/nature10452            

 12 October 2011

Increasing population and consumption are placing unprecedented demands on agriculture and natural resources. Today, approximately a billion people are chronically malnourished while our agricultural systems are concurrently degrading land, water, biodiversity and climate on a global scale. To meet the world’s future food security and sustainability needs, food production must grow substantially while, at the same time, agriculture’s environmental footprint must shrink dramatically. Here we analyse solutions to this dilemma, showing that tremendous progress could be made by halting agricultural expansion, closing ‘yield gaps’ on underperforming lands, increasing cropping efficiency, shifting diets and reducing waste. Together, these strategies could double food production while greatly reducing the environmental impacts of agriculture.

 

The good news is there is an enormous amount of inefficiency in the current system.  Some of it is cultural, some political, some economic - but much of it is the result of doing things the way we have been doing and not thinking.  There is a lot of hope for creativity and we don't have to rely on solutions that may not appear in the necessary timeframe.  If we get busy perhaps we can even save the billion or so people who are starving.

 

breaking the darkness and the danger of goats

Imagine how dark the nights were a few hundred years ago.  I remember reading about a party in the 17th century at a wealthy person's home where the writer commented on the extravagance of the affairs - something like a dozen beeswax candles flickered away on the big dinner table even though the moon was nearly full.    

 

It takes nearly fifty candles to equal the amount of visible light that is produced by a single sixty watt incandescent lamp - even the little fifteen watt lamp in your refrigerator produces as much light as a dozen high quality candles.  Of course low light levels present problems as to what people can do.

 

A la chandelle, la chèvre ressemble à une demoiselle  
  - an old French saying dating from before the 17^th century¹ 

 

The cost of artificial lighting has dropped dramatically over the years. Candles were fairly expensive coming in two basic flavors - beeswax and animal tallow.  Tallow candles required constant work, smelled awful and became rancid, but you could make them from the fat of any slaughtered animal.  Beeswax candles were superior but were so expensive only the church and wealthy individuals could afford them.

 

Oil lamps were extensive and a subject of serious technological progress, but b the time petroleum was discovered in Pennsylvania, a gallon of lamp oil cost about half the wage of the average worker.  Gas lamps were common and expensive in cities at the time and the advent of electric lights, even though electricity cost about one hundred times as much as it does now, adjusting for inflation, was cost effective.  Breaking the darkness was an enormous problem that consumed an enormous amount of money.

 

We had about 20 hours without electricity yesterday and had to make do with some beeswax candles.  To conserve them we only kept three going at a time - and only one in a room at any time.  Story telling is a good diversion for a few hours, but the fact that our gas furnace has an electric fan caused the temperature to drop and electricity at 15 cents a kWh seemed like a fantastic deal.

 

Apart from wishing for warmth it made me think of a few things - 

 

Without electricity you begin to worry about how much energy is left in your mobile phone. Landlines are powered by batteries in the central office and conventional telephony is fairly bullet-proof as long as the lines aren't broken, but many of us now rely on our own batteries.

 

My iPhone 4 has a 1420 milliwatt 3.7 volt battery - about 5.25 watt-hours of energy.²  I have an external battery pack that holds about 20 watt-hours but, of course, it wasn't charged.

 

Five and a quarter watt-hours is not a lot in human terms and tiny compared with the 25 or so kilowatt-hours of electricity the average home uses in a day.  To move that energy into the phone requires a few hours of charging, but it is interesting to compare it to the energy we use in the form of food.    Converting to units we all are familiar with gives about 4.5 nutritional Calories.    A single M&M contains about 3.5 Calories of energy.  Too bad we don't have a little fuel cell from Mars that burns candy.  Then we could pop an M&M in every few hours and forget about the wall plug.

 

It is amusing to compare the power transfer rates we see eating meals and compare that to what our home wiring can provide.  Food can be a remarkably dense form of chemical energy.  (I leave that as a fun little exercise).

 

The back of the envelope was a quick approximation an athlete friend offered.  She isn't technical, but we had been talking about energy and power as we were writing a few pieces and the question of leaving a light on or turning it off came up and my back of the envelope technique has rubbed off on her.  

 

A compact fluorescent lamp needs more power to start up.  How much energy is required and where is the break-even point for leaving the lamp on rather than turning it off (this doesn't consider the cost of a possible failure from turning a lamp on and off - that turns out to be very low for high quality CF bulbs -- there are other factors that contribute to less than optimal lifetimes).  

 

her reasoning...

 

The highest power a circuit in my apartment can provide is about 1800 watts as all of the lights are on 15 amp circuit breakers (power is current times voltage).  Since turning on a lamp doesn't trigger a circuit breaker, 1800 watts is an upper limit for the startup power of a CF bulb.    The bulb needs about a second to warm up, so the startup energy for a CF bulb has to be less than 1800 watt-seconds.  My apartment has four  CF bulbs on a circuit and you can turn them on with the circuit breaker switch and not overload it, so the start up power per bulb upper limit is 450 watt-seconds.  The bulbs are 25 watts each, so it would take them 18 seconds of normal use to equal the 450 watt-seconds of startup energy.  The worst case is the break-even point is 18 seconds and is probably much less.  It makes sense to turn off the lights when you leave the room.  

 

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¹ By candlelight a goat looks like a lady  

           - Thanks to Juliette for the right words.  I'm a poser when it comes to French.  

 

² As rechargeable non-chemical energy storage devices the lithium-ion polymer battery does an excellent job compared to most other technologies.  Moving a 175 pound person about 80 feet vertically stores about 5.25 watt-hours of potential energy in the person.   

 

 

 

 

 

 

the cool of one hand radiating

Your metabolism probably averages something around 100 watts over the course of a day.¹  Our bodies aren’t terribly efficient at converting this energy into motion, so we have to get rid of quite a bit of waste heat.  Sweating is one of the main mechanisms,  It works particularly well when our sweat can evaporate from our skin - something that gets into a bit of curious physics about water. 

 

These mechanisms work fairly well for most of us, but athletes have a real problem.  I’m far from an athlete, but regular produce about 150 watts of work, in addition to my base load, when I’m rowing.  In an hour I’ll go through over a liter of water and will still be very thirsty with my clothes drenched in sweat.  It turns out, if I’m using good form, I’m about 20% efficient so my 150 watts of work requires about 750 watts from my metabolism.  I’m left with about 600 watts of wasted energy to dump somewhere - most of it as waste heat.  Think about holding a half dozen 100 watt incandescent bulbs...

 

Although I have about two square meters of skin, my sweating primarially takes place in preferential areas we’re all know.  At that power level I am still regulating core temperature well and excessive waste heat is not a roadblock to my performance. 

 

Recently I had a bit of surgery and remember being frigid when I started coming out of the anesthesia.  They had wrapped in blankets to deal with the problem, but there was still quite a bit of shivering .  It turns out the anesthesia disturbs our ability to regulate our core temperature and there in lies an interesting story.

 

About 20 years ago a couple of doctors at Stanford noticed you could warm surgery patients by increasing the blood flow to the skin of their palms.  Very very curious stuff indeed.  It turns out one of the ways we control our core temperature is by regulating the blood flow to the skin in non-hairy parts of our body.  Notably the plams, soles of the feet, and cheeks - another neat mechanism.

 

A real athlete often needs to summon a very intense performance and can produce fairly amazing amounts of power.  Those who specialize in events where burst performances are requried are paritcularly impressive.  Colleen can produce over 700 watts for a half minute - a not far off a horsepower.  She is probably about 20% efficient doing this (many of our athletic motions are in the 15% to low 20% range), so she needs to get rid of about three kilowatts of power.  The burner on your electric range on high radiates about half that much.²  One of the limits of intense bursts of powe  - beyond running out of fuel local to the muscle very early on and then developing too much lactic acid shortly thereafter - is the spike in core body temperature.  A world class sprinter would probably die if they were to maintain their power level for - say - 20 seconds.  Their 10 second intense burst of power can raise their core temperature to a dangerous 105°F.

 

If you could artificially increase blood flow in one of the critical areas, you could help dump some waste heat and perhaps increase the endurance of an athlete. It would be great during breaks in football and, in fact, the effect is being exploited with a device known as “The Glove”.  A player inserts his hand into a chamber that seals at the wrist.  A slight vacuum is applied under the palm to stimulate blood flow and quickly drop the core temperature in a few minutes.

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¹ An average adult might require about 2100 nutritional Calories a day.  That is roughly equivalent to 2400 watt-hours.  To find the average power in a day, simply divide by the number of hours in a day.  You’re a light bulb:-)

 

² Of course the hot plate only radiates over an area of about 0.1 meters whereas Colleen has 20 times that area, albeit not evenly distributed.  

 

It was too tempting to use this photo of a very sweaty President. In fairness he probably was the most athletic  

the delight of turning potential energy into kinetic energy

There have been too many weighty events this week - it is time for something fun.  

 

There is something wonderful about watching energy move backand forth betwen potential and kinetic energy even if there aren't many osciallations.  Swings, roller coasters, sailplanes, the arc of a tossed ball, chains of dominos ...

 

You've all seen videos of large domino chains.  By standing a domino on end you are increasing its potential energy.  Energy that can be released later when the domino tips, turning stored potential energy into the energy of motion - kinetic energy.  The key is to find an object that is usually stable, but can tip easily and move its center of mass a long distance in the process.  People make wonderful patterns using thousands of them - but there is another way to spend your day for a few seconds of delight ...

 

Wood is elastic and wants to return to its original position when bent - a property that allowed people to build bows that can propel an arrow at a high speed.  You can use this to store potential energy in a wooden stick.  When given a chance to release the stick will seek its normal shape and the resulting motion is a nice display of kinetic energy.  

 

With a bit of cleverness you can weave a pile of wooden sticks into a structure storing the energy that you used to flex them for later release.  Fifty sticks will give you and idea - a thousand will give you something wonderful.

 

A large number of weave patterns can be used - you just want to construct a regular pattern that bends the sticks enough without moving them past their elastic limit. Craft sticks are recommeded and are inexpensive at a few cents each in quantity.¹  A hundred bucks, a gym floor and a lot of kids would create a dramatic event. 

 

Like many things you can ask a few questions and gain a deeper understanding.  There is enough beauty without the questions, but new delights emerge when you look a bit more deeply.  How much energy is stored in a structure?  What is its energy density? What other materials could be used to improve it?  Could the shape and internal stucture of a stick be improved?   What weave patterns would be optimal? How much of the kinetic energy is turned into sound and heat and how much is goes into the bounce of the sticks?  Could you make a musical version? .. and so on.  Like so many interesting things, this is a rich playground for the mind.  

 

The artist and kid in you might try other weaves, adding some color or even making this part of a Rube Goldberg contraption.

 

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The energy density of mechanical storage systems is not very high compared with other forms of storage the industrial world uses.   Try calculating the energy density of a hydroelectric project as an example.  What about the maximum energy density of compressed air storage? How do these compare to electric batteries and hydrocarbon combustion or hydrogen combustion?  Are you likely to ever see a spring powered cellphone? 

 

On the other hand mechanical energy storage is very useful and even beautiful at the appropriate scale. That scale turns out to be our scale and it is vitally important to many biological systems.   Among other things it lets us run efficiently and makes nearly every sport possible.  To us even a modest amount can seem significant.  An average person on a six story building stores about the same amount of potential energy as the battery in his smartphone, but even that small amount (small for the purpose of running the machines in our lives) is enough be rather unfortunate in a fall.

 

stay curious

 

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¹ stick choice is important. I haven't done this since I was an undergrad, but remember we tried tongue depressors and popsicle sticks - these days you can also buy craft sticks, which I've seen recommended, but I haven't tried.  The amount of "spring" in each of these, their elasticity, varies and will produce very different results.  It probably pays to try small units with a few dozen sticks each before settling on a material for a huge project.

We ended up with tongue depressors mostly because we found a cheap source and made a 500 stick weave.  It was addictive enough that we rebuilt it three times.

 

what is the ground speed of a mediæval soldier?

laden or unladen?

 

Steel plate armor seemed like a great idea to protect soldiers in the days before gun powder, but like anything else there are trade-offs between mobility and protection.  An escalating race between armor and weapons brought about heavy suits that weighed thirty to fifty kilograms by the fifteen century.  Breeding programs for larger cavalry horses became necessary, but finding much stronger people is problematic ...  not to mention the user experience issues associated with trying to work in one of these contraptions.

 

Researchers at the University of Leeds were interested in precisely how much effort was required to move around in all of  that steel kit and partnered with the Royal Armouries to study the impact using real people on an instrumented treadmill. (the paper is behind a paywall) 

 

They found the cost of motion - the work required to move - of a person with a 110 pound metal suit increased by about 2.3 times over an unladen person.  This turns out to be worse than the cost of motion increase for someone wearing a modern  backpack of the same weight due to the distribution of the suit’s weight.  The leg protection amounted to about 20 pounds and it was that swinging weight that contributed to the extra cost.

 

The studies were done on smooth treadmills at room temperature.  Real world conditions that often involved poor terrain would make matters much worse.  This led the authors to speculate on one of the more remarkable military upsets in history - the Battle of Agincourt - where Henry V with a small army of men mostly without armor defeated a much larger French army of heavily armored soldiers. 

 

It happened the fields in the area had just been plowed for Winter wheat and heavy rain showers turned them into mud.  The French had to move across the mud burning huge amounts of energy and tiring in the process - the cost of motion may have been well over four times as high as an unladen person moving through similar terrain.  The asymmetrical use of heavy armor may have been the decisive factor in what should have been a huge loss for Henry. Shakespeare maintained Henry was a great orator who moved his troops to greatness, but such is the privilege of the storyteller.

 

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The cost of motion has been measured for numerous human activities. A nice way to think about this is to consider the power you need to perform an activity above your normal metabolic needs remembering that power is just the energy expended per unit time.  The average person needs about 2,400 watt-hours of energy a day in the form of food (a bit shy of 2,100 Calories).  This corresponds to an average power of 100 watts - you can think of yourself as an incandescent lightbulb equivalent.  We aren’t terribly efficient at converting food into energy our bodies we can use, so we give off much of that in the form of heat.

 

Exercise adds to our input power requirement.  I'm far from an athlete, but I row as a form of aerobic exercise.  Rowing happens to be a nice way to illustrate power at a human level, so if you are willing suffer along I'll detail my exercise story.

 

My rowing machine is an ancient Concept2 Model B ergometer that measures and displays my real power output at a flywheel.¹  When I started to get serious about rowing three years ago I was out of shape and could only manage about 100 watts for ten minutes or so, but with the help of an athlete friend, I've gone to well over an hour at an average power of 150 watts.  This has been a big achievement for me, but is somewhat depressing when you think of the power requirements for stoves, hair dryers, furnace fans and air conditioners.  The scale of human performance differs from the requirements of our modern lifestyles by about two orders of magnitude.

 

A rower in good shape turns food into the mechanical work with an efficiency of about 20 percent.  At 150 output I need 750 watts coming from  food.  Since energy is conserved I'm generating a large amount of waste heat.  Even in the Winter, when the basement temperature is under fifty Fahrenheit, I'm in a tshirt and cutoffs and go through a large amount of water.

 

If you are trying to lose weight human inefficiency is a good thing, although it isn't as good as some would like.  A normal Snickers bar only supplies about about 325 watt-hours of energy.  I need a bit more than two Snickers bars worth of energy for an hour’s worth of rowing.  It is easy to scarf down a few Snickers, but difficult to do that much exercise.  Exercise is good for you, but you have to do a large amount to lose weight.  

 

This chart of my rowing is shows the mechanical work from rowing sessions over a month's time.  The units of work are on the vertical axis and require a bit of explanation.  I'll describe their somewhat messy history in the footnote as it illustrates how creating your own unit system can be ugly and how they can evolve over time.²   Use whatever tracking and motivation mechanism works for you.

 

It takes a lot of time and energy to exercise heavily for long periods.  I rarely go over 90 minutes a day and can only justify the time by using my iPod to time shift some entertainment and news consumption.   When Colleen was training she required north of 5,000 Calories, nearly 6,000 watt-hours of food, a day.  Six kilowatt-hours of electricity goes for less than a dollar in most parts of the country.  Sadly energy in the form of food is much more expensive, although a fine meal is much more pleasant than plugging your body into a wall socket.³

 

Colleen has a lot of explosive power and can easily develop 300 watts for periods of  15 minutes.  Two hundred watts for ten minutes is very difficult for me and 220 is currently impossible.  For very short periods she can burst to much higher levels probably over 700 watts (nearly a horsepower).  She's entirely anaerobic doing this but her fast twitch muscles are not as good as my slow twitch for long periods at lower output levels.  Our genetics can dictate the physical activities we are most likely to survive at intense levels.  Most of us never approach limits so it usually doesn't matter, but it is important for elite athletes.

 

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¹ The Concept2 is a serious piece of kit.  Mine is over 20 years old and still is in great shape with a beautifully smooth and natural motion that give a great user experience.  The brand is used by most NCAA Division I rowing programs as well as Olympic training centers.  A home user is likely to have one for a lifetime and the company stocks spares for all of their older models.  Buy a piece of high quality gear and you're more likely to use it.  The current models are quieter than mine, but the basic mechanism is similar, so if you buy one it is likely to be useful for the rest of your life.  The cost per year over a few decades is very low.  A great company with a great product -  I give them my highest recommendation.

 

²  I was thinking about putting a mark on a stud in the basement noting my progress - a nice visual goal I would see every session and a not so subtle hint.  It occurred to us that a goal could be visualized by equating one minute of rowing at 100 watts of work with an inch.  An hour of rowing would represent a five foot high mark and would be nicely visible on the beam.  I met that goal and new goals changed to our respective heights - one minute of rowing at a 100 watt power level was still an inch.   Slowly I began to regularly achieve the goals at a hundred watts, but I would be running out of room as the basement ceiling is only seven feet from the floor.   It was also time to work on the power level of the workouts as that is a lot of time for an exercise session and she thought she could increase my power output.  We added a literally off the basement chart's  goal for days when the workout is going exceptionally well that represents her standing reach (both feet flat on the ground) of 101 inches.  It is good to have something that always seems out of reach when you start, but there are times when you manage to make it.

 

The new power goals were increased to average to 125 watts and finally to 150 watts.  Each  "minute" now represents 150 watt-minutes of work by this crazy goal-driven history (hey - whatever works to help you visualize a goal).  Rowing for 80 minutes represents 12,000 watt-minutes or 200 watt-hours of work . Divide that by  my efficiency (about 0.2) and you get the food energy I "burned" - 1000 watt-hours or a kilowatt-hour in this case.

 

³ A curious thing to think about is the power transfer rate of an electric outlet.  Most 110 volt outlets in the US are limited to about 1,800 watts of power.  Transferring 2,400 watt-hours takes about 80 minutes at the limit the line can supply.  We can eat the food equivalent in under ten minutes if we want.  The chemical energy in our food is a relatively dense energy store.  This is a serious problem for electric vehicles.  The last mile of the infrastructure is not well matched to high densities of electric cars in residential areas.