1:45 PM - 3:15 PM
[O11-P57] Estimation of solar noon time from observations
Keywords:Sun, Solar noon time, Estimation
1 Motivation and Purpose
It is known that the length of the shadow is the shortest of the day at the time of solar southing. Based on this, we conducted an experiment to determine the time of southing by the length of the shadow of a stick, but were unable to obtain the correct value. We thought that the location where the experiment was conducted had a slope and that the slope was related to the experiment, so we wanted to compare the accuracy on a horizontal location with that on a sloped location and on a horizontal location with a slope.
2 Methods
2-1
The experiment was conducted by recording the length of shadows on paper next to a well-sunlit window facing southwest on the campus of Tennoji High School on six days in February and April 12, 2025. The level was confirmed by a tilting device.
2-1-1
The experiment was conducted once each on February 14, 15, 17, 18, and 20 using the above method. The object to be shadowed was a triangular ruler (transparent, plastic). However, since it was difficult to identify the destination of the shadow, we decided to conduct an additional experiment 2-1-2.
2-1-2
The experiment was conducted a total of five times on February 22 and April 12. Instead of a triangular ruler, we used a mechanical pencil with a 3.5-cm length lead inserted perpendicularly into an eraser.
2-2
On April 12 in Kishiwada City, Osaka Prefecture, in a well-sunlit area, a piece of paper was laid on a flat surface and plotted with the tip of the shadow of a mechanical pencil lead at an incline. One was tilted to the north and the other to the east.
3 Analysis method
The length of the shadow of the object measured to two decimal places (i) and the difference in time since 12:00 (ii) were determined and the equation of the function was obtained in Excel with the x-axis as (i) and the y-axis as (ii).2-1-1 and 2-1-2 data were tabulated and the absolute values of (measured value - literature value) were represented in a histogram. The range of the class was set to 180 seconds, and the vertical axis was set to the number of data. From there, the standard deviation was obtained from the histogram using the formula for standard deviation.
In 2-2, the absolute value of (value obtained in 2-2 - literature value) was examined.
4 Results
From the data on February 22, the deviation from the literature value was kept within 30 seconds. In contrast, the data from the 17th showed a significant discrepancy: the mean absolute value of (measured value - literature value) was 669.4 s from the 10 data obtained in 2-1-1 and 2-1-2. The one tilted to the north in 2-2 showed a discrepancy of 960 seconds, and the one tilted to the east showed a discrepancy of 3540 seconds. The standard deviation obtained from the histograms of 2-1-1 and 2-1-2 was 768 s. When the 17th was excluded as an outlier, the standard deviation was 562.85 s.
5 Discussion
We believe that the reason for the large discrepancy in the data for the 17th is that the times at which the points were taken were all before the sun was in the south. Also, there were variations in the data even when the object was horizontal. This may be because the object was not properly fixed and moved, resulting in inaccurate time measurements, which needs to be improved. We also found that tilting the object in an east-west direction affected the length of the shadow more than tilting it in a north-south direction.
Acknowledgments
Thank you to the Faculty of Science, Kyoto University, and the faculty of Tennoji High School for their advice.
It is known that the length of the shadow is the shortest of the day at the time of solar southing. Based on this, we conducted an experiment to determine the time of southing by the length of the shadow of a stick, but were unable to obtain the correct value. We thought that the location where the experiment was conducted had a slope and that the slope was related to the experiment, so we wanted to compare the accuracy on a horizontal location with that on a sloped location and on a horizontal location with a slope.
2 Methods
2-1
The experiment was conducted by recording the length of shadows on paper next to a well-sunlit window facing southwest on the campus of Tennoji High School on six days in February and April 12, 2025. The level was confirmed by a tilting device.
2-1-1
The experiment was conducted once each on February 14, 15, 17, 18, and 20 using the above method. The object to be shadowed was a triangular ruler (transparent, plastic). However, since it was difficult to identify the destination of the shadow, we decided to conduct an additional experiment 2-1-2.
2-1-2
The experiment was conducted a total of five times on February 22 and April 12. Instead of a triangular ruler, we used a mechanical pencil with a 3.5-cm length lead inserted perpendicularly into an eraser.
2-2
On April 12 in Kishiwada City, Osaka Prefecture, in a well-sunlit area, a piece of paper was laid on a flat surface and plotted with the tip of the shadow of a mechanical pencil lead at an incline. One was tilted to the north and the other to the east.
3 Analysis method
The length of the shadow of the object measured to two decimal places (i) and the difference in time since 12:00 (ii) were determined and the equation of the function was obtained in Excel with the x-axis as (i) and the y-axis as (ii).2-1-1 and 2-1-2 data were tabulated and the absolute values of (measured value - literature value) were represented in a histogram. The range of the class was set to 180 seconds, and the vertical axis was set to the number of data. From there, the standard deviation was obtained from the histogram using the formula for standard deviation.
In 2-2, the absolute value of (value obtained in 2-2 - literature value) was examined.
4 Results
From the data on February 22, the deviation from the literature value was kept within 30 seconds. In contrast, the data from the 17th showed a significant discrepancy: the mean absolute value of (measured value - literature value) was 669.4 s from the 10 data obtained in 2-1-1 and 2-1-2. The one tilted to the north in 2-2 showed a discrepancy of 960 seconds, and the one tilted to the east showed a discrepancy of 3540 seconds. The standard deviation obtained from the histograms of 2-1-1 and 2-1-2 was 768 s. When the 17th was excluded as an outlier, the standard deviation was 562.85 s.
5 Discussion
We believe that the reason for the large discrepancy in the data for the 17th is that the times at which the points were taken were all before the sun was in the south. Also, there were variations in the data even when the object was horizontal. This may be because the object was not properly fixed and moved, resulting in inaccurate time measurements, which needs to be improved. We also found that tilting the object in an east-west direction affected the length of the shadow more than tilting it in a north-south direction.
Acknowledgments
Thank you to the Faculty of Science, Kyoto University, and the faculty of Tennoji High School for their advice.