When the sun is in the zenith and the sky is perfectly clear, the solar power we receive on the surface of the earth is roughly 1 kW per square meter (on a horizontal surface that is normal to the direction of the sun).
Calculate the average solar power per square meter (in Watts) on a horizontal surface for a day when the sun goes through the zenith at noon.
The sun goes through the zenith exactly twice a year on latitudes that are close to the equator. Take the angle to the sun into account.
To calculate the average solar power per square meter on a horizontal surface for a day when the sun goes through the zenith at noon, we need to take into account the duration of daylight and the angle of the sun relative to the surface.
Here's how you can calculate it step by step:
1. Determine the duration of daylight: We need to know the number of hours of daylight on that particular day. You can look up this information for your location or use an online calculator that provides sunrise and sunset times.
2. Divide the day into small time intervals: Divide the duration of daylight into small time intervals, such as 5 or 10 minutes. The smaller the intervals, the more accurate the calculation will be.
3. Calculate the angle of the sun: For each time interval, calculate the angle of the sun relative to the horizontal surface. This can be done using trigonometric functions and the latitude of the location. The angle will change throughout the day, so calculate it for each time interval.
4. Calculate the solar power for each time interval: Once you have the angle of the sun, you can calculate the solar power received on the surface during that time interval using the formula:
Solar power = Solar irradiance * Surface area * cos(angle)
In this case, the solar irradiance is 1 kW per square meter, and the surface area is 1 square meter.
5. Sum up the solar power for all time intervals: Add up the solar power calculated for each time interval to get the total solar power received on the horizontal surface for the entire day.
6. Calculate the average solar power: Divide the total solar power by the duration of daylight (in hours) to get the average solar power per hour. Finally, multiply this value by 1000 to convert it to Watts.
Remember to use the SI unit system consistently and double-check your calculations for accuracy.