Risa Studio

Abstract

An experiment was conducted to test the accuracy of visual observations and analog inclinometer readings. A solar angle calculator was constructed by inputting the trigonometric solar equations into Excel to act as the control to which readings were compared. Data for measurement of solar angles collected from a morning and afternoon of the same day, showed a reasonable level of accuracy with nearly all data falling within a range of 5-15 percent error. The level of error was attributed mostly to user error and the level of graduation of the instrumentation.

Table of Contents

S.No	Description	Page Number
	Abstract	02
1.0	Introduction	04
2.0	Experimental Design and Instrumentation	04
3.0	Experimental Procedure	05
4.0	Theory	06
5.0	Analysis: Data Validation/ Analysis & Error Analysis	08
6.0	Conclusion	09
7.0	References	10

1.0 Introduction:

Using two separate measurement methods [visual observation, inclinometer with magnetic compass] the solar altitude and azimuth were calculated for Phoenix both in the morning and evening. Error analysis was then done by comparing the manual measurements with the calculated angles for altitude and azimuth at those times. Finally, the Excel spread sheet prepared for calculations was used to determine the hours of sunrise and sunset for that day.

2.0 Experimental Design and Instrumentation:

The two instruments used for conducting the experiment were the Magnetic Compass and the Inclinometer. The basic working principle and functioning of the two is as follows:

Magnetic Compass: A compass is a navigational instrument for determining direction relative to the Earth's magnetic poles. It consists of a magnetized pointer (usually marked on the North end) free to align itself with Earth's magnetic field. The magnet is generally called a needle. One end of the needle is often marked "N," for north, or colored in some way to indicate that it points toward north.

A compass works by detecting and orienting itself in a magnetic field. Since the Earth is magnetized, on its surface exists a very weak magnetic field. This magnetic field is a result of the rotational forces of liquid iron in the Earth’s core. Earth can be imagined as a gigantic bar magnet with a North-South orientation that causes other magnetized objects to take on the same orientation. However, Earth’s magnetic North is not the same as its geographic North located at the North Pole, but is slightly to one side. This deviation from true North means compensation must be made when calculating actual directions. These compensation factors vary depending on location on the Earth and can be read from navigational charts.

Inclinometer: An inclinometer is an instrument for measuring angles of slope (or tilt), elevation or inclination of an object with respect to gravity by creating an artificial horizon. It is also known as a tilt meter or tilt indicator. Inclinometers measure both inclines (positive slopes, as seen by an observer looking upwards) and declines (negative slopes, as seen by an observer looking downward).

The inclinometer used for the experiment was essentially a radial protractor with a weighted needle in the centre. If the base of the inclinometer is level, its indicating needle or dial points straight up (i.e.90 degrees). The shadow of the needle on the base gives the reading of the altitude angle of the sun. Aligning the shadow on the dial in an accurate manner with the magnetic compass allows us to take the readings for the azimuth angle of the sun. The readings on the magnetic compass are for magnetic north.

Appropriate corrections need to be made for true north in order to get the final result for solar azimuth angle. In case of Tempe, the correction is 12 degrees from magnetic north/south (sign convention used: negative for morning & positive for afternoon or negative when east of south and positive when West of south).

3.0 Experimental Procedure

a. The experiment was conducted for two different times of the same day on February 1st at 10:15 am and 3:00 pm. The solar azimuth and altitude were first estimated using bare eye and the same were recorded.

b. In the next step, the inclinometer was used to record the solar altitude. This device (which consists of a needle in the centre of concentric circles giving the degree measure for altitude angle calculated based on complex solar geometry), was placed in the sun. The length of the shadow of the nail pointed to the solar altitude (measured in degree) on the base.

d. Next, the magnetic compass (aligned to magnetic north) was placed on the base of the inclinometer in such a way that the shadow of the needle now fell on the compass. Since the solar azimuth angle is the measure of the angle between the line from the observer to the sun projected on the ground and the line from the observer due south, the angle between magnetic south on the compass and the line of the shadow was noted.

d. For Phoenix, the correction required to compensate between true and magnetic north is approx 12 degrees. This correction was applied to the reading taken in step c above to get the reading corresponding to true north. By convention, for mornings we subtract 12 degrees and for afternoons add 12 degrees to get values for true north.

e. An excel spreadsheet was prepared to calculate the solar angles using trigonometric solar formulae. The sheet was used to compare and verify the results recorded from above experiment. Spreadsheet data was used as a baseline to analyze the error associated with observations made by bare eyes and experimental tools.

f. The Sunrise and Sunset time for the day was calculated using the spreadsheets generated.

4.0 Theory

The experiment essentially aimed at understanding the solar geometry and developing the skill to measure solar angles using various methods i.e. using formulae, Inclinometer & Magnetic Compass and through visual analysis. The basic theory behind the solar angles measured is as given below.

Solar Geometry: The tilt of the earth on its axis and our location north of the equator result in sun path which changes throughout the year. The position of the Sun with respect to earth’s surface can be described by two different angles, the solar azimuth and the solar altitude or elevation. Together, the two angles provide useful information about the orientation of incoming sunlight on an object or structure. This information is extremely important while installing solar collector devices and designing building fenestrations and shading devices.

Solar Zenith Angle (θs): Angle between a line pointing to the Sun and the vertical. The solar Zenith angle can be calculated using the formula:

Cosθs=Cosλ * Cosδ * Cosω + Sinλ * Sinδ

Where; λ = Latitude; δ = Declination; ω=hour angle

Solar Azimuth Angle (ϕs): The angle between the line from the observer to the sun projected on the ground and the line from the observer due south. A positive azimuth angle generally indicates the sun is east of south, and a negative azimuth angle generally indicates the sun is west of south. Others define solar azimuth as the angle from due north in a clockwise direction as well. The solar Azimuth angle can be calculated as follows:

Sinϕs= (Cosδ*Sinω)/Sinθs

Where; ϕs = Solar Azimuth Angle; δ = Declination; ω=hour angle; θs = Solar Zenith Angle

Solar Altitude Angle (αs): The angle between a line from a point on the Earth's surface to the center of the solar disk, and a line extending horizontally from the point.

αs= 90 – θs

Where; θs= Solar Zenith Angle

5.0 Data Analysis

Location: Tempe, Arizona Date: 01 February 2010

Inputs	Value	Units		Inputs	Value	Units
Solar Time	9.57	Hours		Solar Time	14.32	Hours
Day of Year	32	Day		Day of Year	32	Day
Latitude	33.43	Degrees		Latitude	33.43	Degrees
Longitude	112.02	Degrees		Longitude	112.02	Degrees
Equation of Time	-13	Minutes		Equation of Time	-13	Minutes
Tilt of Surface	0	Degrees		Tilt of Surface	0	Degrees
Surface Azimuth	0	Degrees		Surface Azimuth	0	Degrees
Outputs				Outputs
Declination	-17.37	Degrees		Declination	-17.37	Degrees
Hour Angle	-36.52	Degrees		Hour Angle	34.73	Degrees
Solar Zenith	61.60	Degrees		Solar Zenith	60.65	Degrees
Solar Altitude	28.40	Degrees		Solar Altitude	29.35	Degrees
Standard Time	10.25	Hours		Standard Time	15.00	Hours
Solar Azimuth	-40.22	Degrees		Solar Azimuth	38.59	Degrees
Angle of Incidence	61.60	Degrees		Angle of Incidence	60.65	Degrees

10:15am Standard Time				3:00pm Standard Time
Results	Altitude	Azimuth		Results	Altitude	Azimuth
Visual Estimate	30	-30		Visual Estimate	25	45
	5.33%	-34.07%			11.44%	-9.09%	error
Inclinometer	27	-43		Inclinometer	20	44
	-5.19%	6.47%			-10.70%	-11.57%	error
Calculation	28.4	-40.22		Calculation	22.14	49.09

Sunrise	6:53 AM	Solar time		7:29 AM	Standard Time
Sunset	5:13 PM	Solar time		5:53 PM	Standard Time

Error Analysis

In addition to a diminished level of accuracy due to imperfection in its making, some level of error can be contributed to the surface which the inclinometer was placed. When placed on a non-level surface the readings of the instrument can be distorted by either the shadow of the nail increasing in length with the instrument tilted away from the sun, or decreased with a tilt toward the sun. Another source of error would be the level of graduation of the inclinometer. With increments of only every ten degrees all measurements which fell between the markings had to be inferred, which carries with it an inherent level of error. The accuracy of the magnetic compass also suffered from its level of graduation as verifying increments proved to be difficult. Both instruments would likely yield a more accurate result with increased scale.

6.0 Conclusions

1. The lab experiment helped in understanding and strengthening the concepts of solar angles. It helped in developing the skill set to use instruments such as the Inclinometer and magnetic compass. The measurements taken using these instruments were cross-checked using the trigonometric equations for solar angles. The two were compared for errors and analysis made to determine possible reasoning for the difference.

2. Data collected from a morning and afternoon reading of the same day, showed a reasonable level of accuracy with nearly all data falling within a range of 5-15 percent error. The level of error was attributed mostly to user error and the level of graduation of the instrumentation.

3. It was concluded that with more accurate and sophisticated instruments, the readings would have been very close to the values obtained using trigonometric functions.

7.0 Reference

1. http://monsterguide.net

2. www.wikipedia.com

3. http://www.teachengineering.org