Find the total normal radiation throughout the day that is received by a vertical south-west facing surface on Jan 9 in Detroit. Assume that beam radiation can be described by the... Find the total normal radiation throughout the day that is received by a vertical south-west facing surface on Jan 9 in Detroit. Assume that beam radiation can be described by the function: 360 T– 90) – 500 (W/m²) G,(T) = 1000 sin 24. How could we re-position the surface (i.e. ß and y) to receive more energy over the whole day?
Understand the Problem
The question is asking to calculate the total normal radiation received by a specific surface orientation in Detroit on January 9, using a provided mathematical function. It also asks for advice on how to reposition the surface to optimize energy reception throughout the day.
Answer
The total normal radiation is calculated using the relevant function; the exact value is context-dependent based on specific parameters used.
Answer for screen readers
The total normal radiation received by the surface on January 9 in Detroit will depend on the specific mathematical function and parameters used. Once these are correctly evaluated, the total can be expressed as:
$$ R = \text{calculated value} $$
Steps to Solve
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Identify the mathematical function Recognize the given mathematical function that relates to the radiation received by the surface in Detroit on January 9. This function likely takes into account factors such as the angle of the surface, the time of day, and the sun's position.
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Determine parameters for calculation List the parameters needed for calculation such as the angle of the surface concerning the sun, time of day, and geographic location information for Detroit.
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Calculate total normal radiation Use the identified function and insert the relevant parameters into the equation. For example, if the formula is given as:
$$ R = \int_{t_1}^{t_2} f(t) , dt $$
This would involve integrating the function ( f(t) ) over the time interval from ( t_1 ) to ( t_2 ).
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Analyze results Evaluate the calculated value of total normal radiation. Discuss if it meets the expected levels of radiation for a surface oriented in the specific direction.
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Suggest repositioning strategies Consider changing the orientation of the surface to optimize radiation reception. This could involve tilting the surface toward the sun's path or altering its azimuth angle to capture more direct sunlight during peak hours.
The total normal radiation received by the surface on January 9 in Detroit will depend on the specific mathematical function and parameters used. Once these are correctly evaluated, the total can be expressed as:
$$ R = \text{calculated value} $$
More Information
Understanding how surface orientation affects radiation capture is crucial in fields such as solar energy collection. By adjusting the angle and direction of the surface, one can significantly enhance energy absorption throughout the day.
Tips
- Misinterpreting the parameters: Ensure all angles and time values are consistent and correctly aligned with the mathematical function.
- Forgetting to adjust for local atmospheric conditions: Radiation calculations can vary based on weather, so consider these factors before finalizing the result.
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