This article explains how to calculate an area-weighted average for lighting, equipment, and people per square foot for a building.
When should I use an area-weighted average for building inputs?
Various factors like lighting and equipment loads vary according to the space functions. In order to account for each factor accurately, it's important to consider the weightage of each factor value based on the size of the space they are applied for. For example, if there is a large-sized auditorium in a building along with a few washrooms and a small office, the factor values for the whole building must be inclined towards the requirements of the auditorium rather than the small office in order to get a clear picture of that particular building. Since cove.tool primary energy simulation is a single zone model, the tool requires a single' whole building variable for each input. To account for zones with multiple products and strategies users will need to simplify these using area-weighted averages.
The weighted average is calculated by taking the summation of "the product of the weights times the data number" divided by "the sum of the weights". If all the weights are same, weighted average is equivalent to the average. The final value, therefore, is a single number representing a list of numbers.
For example, if a student scores 3/5 in assignment 1 which accounts for 30 percent of the total grade and 5/5 in assignment 2 which accounts for 70 percent. The student’s total grade will be the weighted average of the two assignment score as follows.
(30 x 3 + 70 x 5) / (30+70) = (0.3 x 3 + 0.7 x 5) = 4.4 (Higher than the average (=4))
Calculating area-weighted averages for building inputs
Lighting Power Density (LPD)
When the area of the rooms in the building are same, the weighted average will be equal to the mean of the three LPD's. Thus, can be calculated as follows:
LPD = (1.2 + 0.95 + 1.5) / 3 = 1.217
When rooms are unequal in size, to get the average LPD for the entire building, you will need to calculate the area-weighted average. It can be calculated as follows:
//Step 1 would be to calculate the area of the rooms
Room 1 area = 15.5 x 11 = 170.5
Room 2 area = 7.5 x 11 = 82.5
Room 3 area = 13 x 11 = 143
Total area = 396
//Step 2 is calculating the room area ratios
Room Area Ratio = Area of the room/Total area of the building
Room 1 area ratio = 170.5/396 = 0.431
Room 2 area ratio = 82.5/396 = 0.208
Room 3 area ratio = 143/396 = 0.361
//Step 3 is calculating the area weighted average LPD
LPD = Room 1 Area Ratio x LPD 1 + Room 2 Area Ratio x LPD 2 + Room 3
Area Ratio x LPD 3
= 0.431 x 1.2 + 0.208 x 0.95 + 0.361 x 1.5
Equipment load often varies in a building according to different space functions like storage, office, corridors, auditorium. Here is how an area-weighted average for equipment/appliance power density can be calculated for an area with two office spaces and a storage area.
Equipment Power Density (EPD) = Room 1 Area Ratio x EPD 1 + Room 2 Area Ratio x
EPD 2 + Room 3 Area Ratio x EPD 3
= 0.431 x 0.75 + 0.208 x 0.10 + 0.361 x 0.75
People per square foot
Similar to LPD and Equipment loads, the function of a space determines people per square foot. For a standing space, the area required for a person would be less as compared to an office which requires a workstation for each employee. Thus, the average number of people per square foot can be calculated in a similar way.
People per square foot = Room 1 Area Ratio x P/sq. ft. 1 + Room 2 Area Ratio x
P/sq. ft. 2 + Room 3 Area Ratio x P/sq. ft. 3
= 0.431 x 0.02 + 0.208 x 0.005 + 0.361 x 0.003
It can be seen that since the area for Room 1 was more along with the person per sq. ft. value, the average value is more inclined towards the same which wouldn't have been the case if Room 2 had 0.02 person/sq. foot. This shows the importance of area-weighted averages.
Envelope & Window-to-Wall Ratio
The same area-weighted average principle can be applied to envelop properties. If your building envelope has multiple walls and glazing products and cove.tool only allows for a single input factor for the entire building, then calculate the whole building R-value, U-value, and SHGC value for each category. This does not apply to VT%, instead, users would model geometry in front of glazing as explained in the Frit Patterns analysis article.
User's can also calculate their window-to-wall ratio (WWR%) using the area-weighted-average method. Using cove.tool's manual inputs on the geometry page, user's can calculate WWR% using either of the following methods.
WWR% = Total Glazing Area (sq. ft.) / Total Exterior Wall Area (sq. ft.)
WWR% = ( (N. Exterior Wall Area (sq.ft.) x N. WWR%) + (S. Exterior Wall Area (sq.ft.) x S. WWR%) + (E. Exterior Wall Area (sq.ft.) x E. WWR%) + (W. Exterior Wall Area (sq.ft.) x W. WWR%) ) / Total Exterior Wall Area (sq. ft.)