Theory/Solar vs Gasoline:

Solar Insolation is a term that refers to the amount of energy radiated from the sun onto a given surface in a given amount of time. Often in the field of Photovoltaic’s this is given in watts per square meter of panel or kWh per square meter per day.

To simplify the discussion of insolation, a unit of ‘one sun’ is defined as the light power that is received by one square meter under optimal conditions. If you remember from Lesson 3, that is 1,000 W/m^2 and one sun-hour is the amount of energy that is radiated onto a square meter surface by a full sun for the duration of one hour (note, it is equal to 1 kWh for a square meter). The origin of this unit of one sun is related to the average solar irradiance that falls on a surface perpendicular to the sun at sea level on a clear day, at noon. This value is a derivative of the solar constant.

The solar constant, which for most practical applications is constant, is the quantity of irradiative flux that is incident on the top of the atmosphere and is generally accepted to be 1,366 W/m^2. This irradiation is the maximum insolation the earth surface would see if no losses occurred due to absorption and reflection of energy via the atmosphere and cloud cover. On average, the atmospheric losses bring the sea level insolation at noon to the 1,000 W/m^2 we discussed earlier. When we account for the fact that the suns direct rays are less intense in the morning and evening and effectively zero at night, a daily average of 250 W/m^2 is often used for the most basic estimations of PV systems.

Of course, this number depends a lot on the location. In terms of sun-hours this means that a decent location will get roughly 6 sun-hours per day (250 watts for 24 hours or 6 hours at one sun). Below is a map of insolation in full sun-hours around the world. Notice the high potential areas in the Sahara Desert, New Mexico and parts of Australia.

Sun-hours of solar energy

World Insolation Map: expected number of full sun-hours you can expect in different locations. 1 sun-hour equals 1 kWh per square meter per day (source: www.global-greenhouse-warming.com).

Light Bulbs and iPhones

Now we need to understand what we can do with this amount of energy: lets look at what devices we can use/charge using a small solar array. We will use a one square meter panel as an example for these basic calculations. If we were to set up a 1 square meter PV array with a conversion efficiency of 12%, we collect enough energy to operate a 100 W light bulb at full power for 6 hours per day. You can get an idea of efficiency by comparing the light that you might get from a 1 square meter sun roof to that of one 100 watt light bulb. Alternatively, if we had some sort of energy storage system connected to the same array for one day, we could charge more than 100 iPhones! (one iPhone's charge is 0.0043 kWh, or 1,150 mAh at 3.7 Volts).

Now, the amount of energy stored in an iPhone is relatively small. Lets make a comparison with gasoline and figure out how long it would take our same system to produce the equivalent amount of energy stored in one gallon of gasoline. Taking the energy content [higher heating value] of gasoline to be on average 34 MJ/liter or 132 MJ/ US gallon (37 kWh per gallon!) it would take our system !60 days! to collect the equivalent amount of energy stored in gasoline. This is why we call fossil fuels ‘energy-dense’. However, when we want to convert the energy contained in the gasoline to electricity (the same output as the solar panel), we lose roughly two-thirds of the energy in the gasoline. You might think: after all the years of development of engines, we still only get 33% efficiency?! It seems low, but the truth is that there is a limit to the theoretical efficiency of converting heat to electricity. Still, even though you lose a lot of energy in the form of heat, it is still huge compared to the energy you get from a solar panel.

The weight of storing energy

Obviously, if you don't immediately use the energy you generate with your solar panels, you need to store the electricity. Let us now look at a few batteries and see how they compare on the energy density (energy per weight) with gasoline.

Type MJ/Kg Application
Li - Ion 0.6 iPhone
NiMH 0.4 Prius
Alkaline 0.6 Duracell Rabbit
NiCd 0.14 RC cars
Lead Acid 0.14 Cars' lights, engine start
Gasoline 45 Become oil-dependent :)

As we can see in this table, battery technology is clearly far behind liquid fuels in terms of energy density and compactness: to store the same amount of energy as in gasoline, the batteries would weigh a little less than 100 times more. This is one side of solar energy and transportation that not everyone fully understands. The incredible energy density of liquid fuel and the amount of energy that is required to operate a car is often overlooked due to the low price and high availability of gasoline. Think about it: if we want to drive a typical electric car 20 miles, we will have to charge batteries with our 1 square meter panel for 50 days (or 50 square meters for 1 day). If we were to drive the gasoline version of this car, we would only need ~1 gallon of gasoline!

So we will be getting about 3-4 miles/kWh and we will be able to produce about 35-40 kWh per day with a 55 square meter array. This will allow us of a range of 160 miles per day provided we get typical insolation of summer months. This shows us how much more efficient electric cars can be compared to gasoline cars which have large thermal and friction losses.

It should be kept in mind that this gasoline has been in the making for millions of years and we have a finite amount of it, where for all intents and purposes we have an unlimited supply of solar energy, the sun is not going anywhere soon (or at least we hope not).

Regards,

Garrett

 


 

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