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Kyoto Box Optimization with the Sun at the Zenith

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Please see attachment. I am having difficulty understanding what the optimal angle (theta) is.

Kyoto box is a simple solar oven used extensively in Africa. Assuming a square box with four reflectors of L = 75 cm, on a sunny day with direct sunlight from the zenith, what is the optimum angle ϴ? What is the total solar power received by the box? If the efficiency is 70%, how long will it take to heat 1 gallon (3.785 liters) of water from 25°C to the boiling point?

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Solution Preview

The explanations are in the attached file.


Since no other dimensions are given, we assume that any ray that hits the Plexiglas plate is absorbed to heat the water.
The angle is optimal when the vertical ray (darker blue) hitting the outer end of a mirror is reflected to the outer end of the Plexiglas darker (green line is the reflected ray).

Since the triangle formed by the green ray, mirror, and Plexiglas is isosceles, both the sharp angles are the same and ...

Solution Summary

This solution finds the optimal angle for the Kyoto box mirrors when the sun is at the zenith and calculates the time needed to bring water to boiling.