Publication Date


Document Type


Committee Members

James Menart, Ph.D. (Advisor); Scott Thomas , Ph.D. (Committee Member); Mitch Wolff, Ph.D. (Committee Member)

Degree Name

Master of Science in Renewable and Clean Energy Engineering (MSRCE)


The amount of cloud cover present in the sky is a significant factor when determining the solar radiation impinging on a solar panel. The optimum tilt required to achieve maximum energy impingement on a surface is also influenced by the amount of cloud cover. This work presents a method for determining the optimum tilt angle for a fixed solar panel when a set amount of cloud cover is present in the sky. Fixed tilt angles that have the most incident solar energy over the course of a year as a function of cloud cover, latitude, and azimuthal angle orientation are calculated for the entire world, the entire range of cloud covers, and the entire range of azimuthal orientations. Maximum intercepted energy is also presented. A trigonometric, integral equation is derived to determine the optimum tilt angle. This derivation was done as a continuation of prior work performed at Wright State University on optimum panel tilts for no atmosphere and clear sky conditions. The model developed here is different in that it includes the effects of the change of panel sunrise and sunset with panel tilt. In comparing results calculated with this effect to those without, it was determined that including panel sunrise and sunset change with tilt has no significant impact on the optimum tilt angle or intercepted solar energy. This is beneficial because the complexity added to the model by including this effect is substantial. In addition to deriving a more complete optimum tilt angle equation, clear sky models for beam and diffuse transmissivities from two different sources are combined with cloud cover models from a third source. It is felt that this combination of models results in more realistic beam and diffuse transmissivity models than using the recommended clear sky models. Using this combination of clear sky and cloudy sky transmittance models required adjustments to the cloud cover model. These adjustments are clearly described in this thesis. The resulting model is capable of calculating optimum tilt angles and maximum intercepted solar energy for sky conditions from clear to completely overcast. Complete results of optimum tilt angles and maximum intercepted energy are presented. A more complete presentation of the effects of cloud cover on optimum tilts has not been found in the literature. These studies are done for the entire world from the south pole to the north pole as a function of latitude and azimuthal orientation. As expected the results show that increasing cloud cover always reduces the maximum solar energy intercepted, with a faster decrease as the amount of cloud cover increases. The optimum tilt angles decrease as the cloud cover increases, going to a horizontal orientation for completely overcast skies. The highest intercepted energy is always found when the panel is pointing due south in the Northern Hemisphere and due north in the Southern Hemisphere. The optimum tilt angles are also the highest at this azimuthal orientation. As the panel is shifted away from this azimuthal orientation, the optimum tilt angle and the optimum energy values decrease. Near symmetry in the optimum tilt angles and maximum intercepted energy is found between the Northern and Southern Hemispheres and between easterly and westerly orientated panels. Along with cloud cover conditions that are uniform throughout the year, studies are done on semi-annual cloud changes and semi-daily cloud changes. Semi-annual cloud changes deal with different amounts of cloud cover over the two halves of the year, the winter half and the summer half. Semi-daily cloud changes deal with different types of cloud cover before solar noon and after solar noon. Interesting results are obtained with these cloud cover profiles.

Page Count


Department or Program

Department of Mechanical and Materials Engineering

Year Degree Awarded