Solar geometry calculator

Name: ______________________________ AE220 – Summer 2017

Lab Assignment 2 – “Solar Geometry Calculator” Due: Monday, 8/28/2017, 10:00 a.m. in class

Objectives:

• Further our understanding of solar geometry through practical application, i.e. the development of a solar angle calculator.

• Become familiar with developing a custom tool based on theory.

Create Excel Tool:

Create an Excel workbook that will take certain inputs and calculate the resulting solar angles. You are free to be as creative as you like in terms of how your calculator is formatted in Excel. Inputs:

• Local Standard Time (tstd) or Clock Time [24 hr format] • Month (1-12) [no.] • Day of Month (1-31) [no.] • Latitude [degrees] • Longitude Standard (Lstd) [degrees] • Longitude Local (Lloc) [degrees] • Tilt of Surface (��) [degrees] • Surface Azimuth (��) [degrees]

Outputs:

• Day of the Year Number (1-365) [no.] • Declination Angle (�) [degrees] • Equation of Time Coefficient (B) [degrees] • Equation of Time (Et) [minutes] • Local Solar Time (tsol) [hours] • Hour Angle (�) [degrees]

• Solar Zenith Angle (��) [degrees] • Solar Altitude Angle (��) [degrees] • Solar Azimuth Angle (��) [degrees] • Solar Incidence Angle on Surface (��)

[degrees]

Deliverables:

• Excel File: log the solar altitude and solar azimuth angles for the daylight hours of the 21st day of each month for Philadelphia. Plot the solar altitude angle vs. the solar azimuth angle. The goal is to create the sun-path diagram for Philadelphia (see the sun-path diagrams in the lecture notes).

Notes:

• Excel’s trigonometric functions use angle measurements in radians and NOT in degrees. Therefore, in your calculations you will need to convert all inputs that are angles in degrees to radians using the conversion 180° = � radians� or by using the RADIANS() function in Excel. Outputs will similarly need to be converted from radians back to degrees.

• Ignore daylight savings time for this project. • For the solar azimuth angle, use the following equation to avoid errors with taking the inverse sine. Note,

you will need to manually input the sign convention to the output of this calculation (negative for east-of- south, positive for west-of-south).

cos�� = sin �� sin � − sin �