How much surface area?

Question

The best solar panels currently available are about 13% efficient in converting sunlight to electricity. A typical home will use about 40. kWh of electricity a day. Assuming 8 hours of useful sunlight per day, calculate the minimum solar panel surface area necessary to provide all of a typical home's electricity.
Energy rate of sun = 1.0 kilowatt per square meter of surface area.

Thanks

Answer 1

E = 40 kWh = 1.44E+8 Joules
dt = 8 hours = 28800 seconds
I = 1000 watts / m^2

A = E / (I eff dt)
A = 1.44E+8 J / (1000 W/m^2) (0.13) (28800 s)
A = 38.46 m^2

I think you're being optimistic about the solar flux at Earth's surface. In space, the bolometric (whole spectrum) flux is 1360 watts per square meter normal to the sun.

Answer 2

hi.

40kWh of energy per day translates to average 1.6667kW power consumption at all times. that is found by dividing the days ernrgy consumption by the number of hours in a day, since the time unit for kWh is h.

now since the power production of the solar panel is only active during the 8 hours of sunlight, it is only proudcing energy 1/3 of the time(8/24). the average power production is 1.0/3, or 0.333kW.

we need to know the average because energy consumtion occurs for all 24h whereas energy production only occurs for a fraction of that.

true power production is much lower because of the low efficiency. you end up with a practical 0.0433kW per sq m power rate.

no. of sqm requires is 1.667/0.0433= 38.5


to explain in another way, if you used1.667 sq meters of solar panel to meet the power needs of 1.667kW, you would end up short because you wouldnt have any power for 16h of the day, also 13% efficiency means you wouldnt have any power for about 23h!

Answer 3

The maximum area for a pixel using the slope method was much higher compared to the SHR method. This indicated that the SHR method was not sensitive to extreme slope values, which is natural owing to its dependency on neighbouring pixel values. Pixels with 0 slope value should ideally yield an SHR value of 1, which is actually not evident from the first record of Table 2. The reason is again attributed to the fact that SHR for 0 slope pixels were dependent on slope of neighbouring cells.