2018-02-03

Electric Cars on the Back of the Envelope

During my Massage Today...
My therapist and I got to talking about electric cars and how California is trying (again) to get electric car use up to meaningful levels, e.g., 30% by 2030 or something.

I Can Never Remember...
How much energy is incident on one square metre of the Earth's surface? Since I was lying there naked, without even access to Google (the horror, oh the horror), I tried to work out a quick approximation. How about we assume a 100W light bulb is 5cm in diameter, and that we make a one metre square filled in with 20 bulbs to a side, i.e., 400 x 100W light bulbs.

💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡 💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡💡

In other words, 40,000W or 40kW. For the sake of brevity, I assume that the brightness of the Sun on a one square metre of surface at noon is of similar brightness, hence the energy available from the Sun is approximately 40kW per square metre, or 40kW/m2

In other words, on a one square metre of surface (at noon, say), you can get forty kilowatts of power (at 100% efficiency).

Energetic Economic Convergence
Say what...?! I rode in my brother-in-law's Tesla last month and it seems that the cost of energy to charge up his Tesla at the charging station is comparable to the cost of gasoline for a gasoline car. Rather than doing all the physics of energy of motion and such, let's just take how much it costs me to drive my commute and assume that the electric energy required, however much it is, costs the same as the gasoline I currently burn. This should be a reasonable assumption since the typical consumer is only going to switch to electric cars once the cost reaches parity (assuming comparable convenience).

Let's check the numbers:

My daily commute is 30 minutes each way, or one hour total
I commute 20 working days per month.
I spend, say, $20 per month on gasoline
Electricity costs 10¢ per kW/hr
Incident power from the Sun is 40kW/m2

So how many kilowatts do I use per month, and how much does that cost? If we assume that my $20 commuting cost in gasoline translates into the same cost in electric power, at 10¢ per kW/hr, we get 200 kW/hrs of electric power for me to commute each month.

If I have 20% efficient solar cells on the top of my car, even just a square metre of them, can I collect that amount of power for free, either while my car is parked at work, or even while I'm driving?

With 20% efficiency, I'm only getting 8kW per square metre of power from the solar cells on top of my car. Is that enough? I'm only using 10kW/hrs per day on my commute of one hour, so one square metre of cells could collect 8kW/hrs of power during my commute (if it's at noon).

With this set of assumptions, it looks like not only could I easily charge my car completely while it was parked while I was at work, with only one additional square meter of solar cells on the car, I could poetentially run the car indefinitely without having to stop to charge at all!

Summary of Assumptions
My back-of-the-envelope, lying-naked-on-a-massage table assumption for the solar power per square metre of sunlight is a wild guess that a square metre filled in with 100W lightbulbs would produce similar brightness, hence, power output.

My other assumption is the cost of the amount of power required for a month's commute is the same for gasoline as for electric power. My Tesla example suggests that this is already true, i.e., that you pay the same to charge your Tesla as you do to fill your gas tank to take you the same distance. My further assumption is that this cost translates into an amount of power based on current electricity prices, which in turn plugs into the lightbulb analogy to yield charging energies and times.

All we need now are electric cars that are as affordable (or moreso!) as gas cars, and manufactured in sufficient quantities for them to be a viable choice for most or all consumers. Nothing suggests this is impossible or even particularly difficult -- the Teslas out there now are very high-end luxury cars. They're not expensive because they're electric, they're expensive because they're expensive.

Industrial Benefits
If you are good at producing internal combustion engines...then you're good at producing internal combustion engines, which are only good for a few things, mainly powering gas cars. The technology for doing so is primarily from the Nineteenth Century.

However, being able to make large numbers of electric motors of all sizes, weights, power output, precision, etc., translates into everything.  All forms of technology, both industrial, military, and civilian, from cars (we hope, and soon, please), trains, electric generators, factories, refrigerators, electric toothbrushes, washing machines, etc. use electric motors. Having a lot of manufacturing base and expertise in making these translates into massive process refinement and workforce sophistication.

Did anybody say "exports"?  How about economies of scale and efficiency savings?

The City Effect
If you assume that the typical American western city is about 50% paved with asphalt, and some 10%-50% of that surface is covered with cars, including cars driving and/or stuck in traffic as well as parked. With 20% efficient photovoltaic cells covering those cars, 50% paved surface times 50% covered with cars at 20% efficiency yields approximately 4% of the total energy from the Sun hitting (and heating up) a city like Los Angeles could be absorbed and converted into motive power for automobiles.

Think about it. 4% of the heat energy absorbed. This could translate into a 102° day turning into a 98° day. If climate change is, say, increasing the average temperative by 1° to 2° per year, electric cars with solar cells on their roofs could offset that.


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