Opaque, vertical and horizontal exterior shading elements (right) can be modeled with EnergyPlus. LBNL researchers are developing new tools that will enable routine, more accurate modeling of non-coplanar shading systems made of optically complex or light-scattering materials. For those that use a non-opaque material, EnergyPlus currently assumes a hemispherically diffusing, solar-optical output distribution, which is a good approximation for a fabric awning but not for a louvered overhang. Simulation tools such as EnergyPlus can model opaque non-coplanar systems (e.g., an overhang made of solid metal). LBNL researchers are working with industry to characterize and measure the window heat gain and daylighting performance of these systems. Some systems, such as the drop arm awning, are operable. The shades themselves are often specified with non-opaque materials such as fritted glass, punched metal, expanded metal mesh, or fabric. These systems provide a relatively unobstructed view while shading the window from direct sun. Implications to the assumed stability of observed planetary systems.Exterior shading such as overhangs, fins, and awnings that project from the plane of the façade are called non-coplanar shading systems.

System scale and the initial inclination of the planets. The fraction of long lived systems is dependent on the absolute Inclinations can continue to evolve for over 1,000 times longer than theĮncounter time.

Systems with non-zero mutual inclinations survive after a close encounter andĭo not promptly experience a planet-planet collision.

We investigateīoth the time to the initiation of instability through a close encounter and We carry out N-body integrations on a large number of systems withĮqually-spaced planets (in units of the Hill radius) to determine theĭistribution of instability times for a given planet separation. Reshaping of the system's architecture via planetary collisions or ejections. After aĬrossing, the system enters a period of chaotic evolution ending in the Steffen Download PDF Abstract: Planetary systems with more than two bodies will experience orbital crossingsĪt a time related to the initial orbital separations of the planets.

Not coplanar