it's not easy being green

The lovely little cherry in front of our place says Spring is finally here.  It's beginning to leaf and currently is generating a bit north of a watt per square meter.  In a few weeks it will  throttle up to max cherry tree power.

 

Photosynthesis generates about three times as much energy per year as humanity uses. All of our food and most of the energy we purchase comes from it, but we usually don't walk by a tree and think - oh what a lovely oak and such a sunny day.  It's probably up to three or four hundred watts at the moment.¹   Photosynthesis never had to be extremely efficient, and it never evolved to anything close to the theoretical maximum.²   SciFi films sometimes show green skinned aliens who do photosynthesis, but it would be barely enough to charge their phones - if you were close to nude you'd be lucky to present a square meter  If you spent your time outside every day  might average about 25 watt-hours a day -- maybe a watt of power.  But throw on clothes and go inside and it falls apart quickly.  Anything that moves around and has a brain can't easily harvest power passively -- storage key to our existence.

 

For an idea of scale you need about a hundred watts of power to run your body - that's close to 2,000 nutrition calories a day.  If you could plug into a tree with perfect efficiency, you'd need a good sized one to keep going.  We do this by eating green plants or things that green plants eat, but you begin to get an idea of scale. 

 

Systems of all flavors and change radically with scale and purpose.   A car is a wasteful means of moving a person around ... payload to gross vehicle weight is often under five percent while something like a bicycle  is usually above eighty five percent.  Since most of us are unwilling and unable to spend more than an hour a day commuting and we like traveling by ourselves,  a car gives convenient range and energy costs have been low enough to justify enormous growth of the transportation mode.    

 

Now everyone is talking about autonomous vehicles.  Many assume we'll see something like Teslas or other conventional electric vehicles with the appropriate sort of computation.  I've written about such things - get in touch or check out Horace Dediu and Jim Zelmer's excellent Asymcar podcast.  Moving people in cities doesn't scale with payload to GVW ratios below a third or so.  Rethinking the vehicle is essential and there are reasons to think something like it could happen. 

 

I've done some work looking at single and two passenger vehicles with GVWs under 500 kg - sometimes much smaller.  If you keep the speed under about 40 km/h you're fine for most cities with good crash survivability and less expensive autonomy. Electrics and regenerative braking are a must in this regime, but aerodynamics are unimportant. Parking is a much smaller issue and navigation is easier.  Hybrid navigation schemes involving buried cables can happen.  With modest engineering thirty plus year life cycles outside of batteries and tires is possible, so you would probably wouldn't own one.   Not that this would happen, but it is probably much more practical than the Uber/autonomous schemes.   There are still some rather large social, data ownership, security and privacy challenges and none of this is going to happen overnight - the timescale of fleet replacement is about an order of magnitude longer than smartphones.  Along the way we're likely to see much of what we have now with much more computation for safety.  

 

Rather than write a book on the subject I'll stop here, but if you're interested there are reasons why the future could be different from the popular vision - in fact historically it almost always is.

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¹ There are a couple of ways of getting at this.  The quickest is to consider the surface area of the tree covered by leaves - the two dimensional cross section normal to the solar direction is a good first approximation, multiply that by the solar power per square meter at the time.  On a clear day at altitude with the Sun perfectly overhead it's about a kilowatt per square meter, but usually it's 500 watts per square meter or so in the Summer on a clear day at mid latitudes...  averaging for clouds and night and solar scatter gives you 150 to 300 watts per square meter in mid latitudes... about 240 world average.   Now plug in the photosynthetic efficiency of the tree..  generally 0.2 to 0.5 percent for deciduous trees.

Another way is to look at the biomass tree produces in a year and recognize the metabolic needs of a tree aren't huge.  It isn't moving around or thinking. 

° the average solar energy per day for this part of the country for April through September is about 4 kWh/m² per day and trees are in leaf about 220 days a year.  

° an average mature oak is about 50 feet tall.  I approximate the leaf area by a disk with a radius of 6 meters or an area of about 100 m²

this → 88,000 kWh for the oak per leaf season

° a 50 foot oak has a dry mass of about a ton - I'll call it a metric tonne.  It produces about 100 kg of new dry wood a year

° dry wood has an energy content of about 16 MJ/kg or about 4.4 kWh/kg

this → 440 kWh of energy from the dry wood and an efficiency of 440/88,000 or 0.5%

440 kWh/leaf season → 440kWh/(220 d * 24h/d) or a bit over 80 watts average

² Caltech is working on that one

 

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Vegan Meringue

 

I'm not kidding...  I tested the claim that you can substitute the brine from chickpeas.  Here's what worked .. better is probably possible.  I've had a couple of edible disasters and a couple of successes .. the trick on the oven door is important!

 

Ingredients 

 

° 6 Tbl of brine from canned chick peas 

° 1/2 tsp cream of tartar

° 3/4 cup of fine sugar (the finer the better)

° bit of salt

° 1 tsp vanilla extract

 

Technique

 

° oven to 250°F

° in a mixing bowl wisk the brine and cream of tartar with an electric mixer for a few minutes until it foams.  Add the sugar a bit at a time and keep wisking, when the sugar is mixed in add a pinch of salt

° as peaks begin to form mix in the vanilla after an eternity - over ten minutes for me - stiff peaks formed. 

° pipe it to a cookie sheet and bake about 45 minutes.  You need to do the meringue trick of not opening the door - just turn off the heat - for an hour or so to let them dry.  

 

Comments

[Jheri]

You're the only person I know who would think about the wattage of a tree;)

and that's a good thing

[David]

I would love to hear your take on autonomous minibusses with space for 8 to 12 passengers or so, moving about at 25 to 40 km/h. Far heavier but otherwise they fit the bill. It seems to me they won't work in the American suburb with its subdivision dead-end roads and longer distances between housing. But in Asia and Europe in large cities with train networks they just might as a connection to a transport node.

[steve]

Indeed - that's an active area of consideration. It depends on the city, but is mostly an urban solution with some existing mass transit and very limited parking and low low occupancy vehicles. ..Population densities of 20k per square km and up seem most appropriate. Synchronization with other modes of transit are important.