The MDI ECR Calculator provides a simple form for calculating Effective Cavity Reflectances (ECR) values and storing the specified data in a file.
The available actions are presented in the line of command buttons across the top. 'Calculate' uses the current form data to calculate the corresponding ECR values. New or existing files can be opened or saved using the corresponding command buttons, 'New', 'Open' and 'Save' (which also calculate the ECR value).
Effective Cavity Reflectance (ECR) is a numerical representation of the reflectance of a cavity of specified dimensions and using two averaged reflectance values: one for the base (opposite the opening) and one for the sides. Typically the cavity is described as rectilinear, using orthogonal dimensions of depth, length and width. ECR values are used in the Lumen Method when 'hiding a cavity' behind a virtual plane i.e. replacing a cavity with a virtual surface having the same effective reflectance as the cavity.
The MDI ECR Calculator offers both the conventional calculation, using the rectilinear dimensions of length, width and depth, and also an alternate calculation using depth with values for the perimeter and base area. This alternative calculation is chosen by checking the alt calc checkbox. This version allows for spaces such as round skylight wells to be evaluated. The alternative calculation does establish temporary values for length and width, but does not save them.
Length and width relate to the cavity opening and depth is the distance from opening to base. The corresponding values for perimeter, base area and cavity ratio (CR) are shown.
For the alternate calculation, the depth is still the distance from opening to base, the length of the perimeter corresponds to the distance around the opening, and the area of the base matches the area of the opening.
For cases where the opening and base do not have the same area, the special case calculation discussed below may provide an estimate.
Base refers to the reflectance of the base surface (from 0.0 to 1.0), and Sides refers to the average reflectance of the sides of the cavity.
This ECR calculator uses either cavity dimensions or perimeter-and-area specifications in the calculation, but sometimes the available information is the area of the cavity opening and the area of the surface inside the cavity. The most familar example of this situation is the inside of a dome. This is a special case for which this calculator does not work, but the ECR value can be calculated using a simple algebraic formula:rhoEff = 1 / [1 + ((As/Ao) * ((1 - rho)/rho))]
For example, for a hemispherical dome with radius of 20 (feet or meters), As/Ao is two (always for a hemisphere, specifically 2,513 / 1256.6). For surface reflectance at 0.80, the effective cavity reflectance = 1 / (1 + 2*(0.2/0.8)) = 0.667. This can be checked using the ECR calculator by using equivalent areas: the values of As and Ao for a dome with radius of 20 correspond to length and width of 35.45 and depth of 8.86 (feet or meters).