The purpose of the post is to help calm my anxiety that this very useful information might be lost should the original source page disappear and to provide a validated, concrete example of its application. I offer my thanks to the author, software engineer Charles R. Landau, for precisely quantitating what I empirically knew to be true during my years as a solar designer and installer.
For northern latitudes between 25° and 50°, the following equations are the essential distillation of Charlie’s article. Scroll down to his section – Adjusting the tilt four times a year:
- March 5: tilt angle 1 = 0.98*latitude – 2.3°
- April 18: tilt angle = 0.92*latitude – 24.3°
- August 22: tilt angle = 0.98*latitude – 2.3°
- October 5: tilt angle = 0.89*latitude + 24.0°
I always advocated changing panel tilt twice per year on the Equinoxes. He has that covered as well. Scroll down to his section – Adjusting the tilt twice a year:
- March 30: tilt angle = 0.93*latitude – 21.0°
- September 10: tilt angle = 0.875*latitude + 19.2°
At first, I found it fascinating that his tilt dates do not fall on the Equinoxes. But, of course they don’t(!) since his calculations account for the fact that days are longer after the spring Equinox and before the autumn Equinox. His explanation of tilt angles is also worth repeating – “…we are considering the whole day, not just noon. In the morning and evening, the sun moves lower in the sky and also further north (if you are in the northern hemisphere). It is necessary to tilt less to the south (or more to the north) to collect that sunlight.” Intuition tells you that this so, but actually quantitating it is another matter. Scroll down to his section – How these numbers were calculated, and pause to consider the complexity and beauty of the science and its thoughtful application.
Thanks Charlie. Totally awesome.
Here’s a (validated) result for Santa Fe, New Mexico at latitude 35.7°:
- March 5: 32.7°
- April 18: 8.5° ←remarkably shallow angle!
- August 22: 32.7°
- October 5: 55.8° ←better for snow shedding!
- Output 2: 7584 kWh
Or, if tilting just twice a year:
- March 30: 12.2° ←still remarkably shallow!
- September 10: 50.4°
- Output: 7543 kWh
Compare this to the common recommendation of tilting to latitude +/-15° on the Equinoxes:
- March 21: 20.7°
- September 21: 50.7°
- Output: 7504 kWh
- A 0° tilt is a horizontal panel (lying flat on level ground). A 90° tilt is a vertical panel (like a typical window pane in a wall). ↩︎
- Calculated using PVWatts to generate monthly energy output data at the relevant tilt angles for Santa Fe NM. A simple spreadsheet was used to prorate monthly outputs which were then summed (combining the various tilt angles) for an entire year. Web page defaults were used for all other parameters (4 kW system, standard module, fixed (open rack), 14.08% loss, 180° azimuth). ↩︎
