## 711 Weighted Centroid Method

The weighted centroid method is similar to the basic centroid method except that this method assumes that the point subject to the longest duration of fire, and consequently the most severely damaged, is the point of origin. To this end, areas more severely damaged by fire are given more weight in determining the centroid than areas with less severe damage. As before, the method presumes a generally homogeneous structure in terms of material flammability and construction.

For example, the various fire-damaged areas can be divided into severity zones, with the most severe areas of burn damage given a weighted factor of "10." Areas with less severity of fire damage are assigned lower weighted factors as shown in Table 7.2. Areas with no fire damage are assigned a weighted factor of "0" and drop out of any equations.

A sketch of the building can be made drawing in the various areas that have been damaged. When the weighting factors are applied to the various areas, the resulting burn damage sketch will appear somewhat like a topographic map with contour lines. Whereas the contour lines in a "topo" map indicate elevation, the contour lines in the fire sketch indicate fire severity.

The centroid of the fire-damaged area can then be found by applying the weighting factors to the various areas affected. The equations for the determination of the centroid coordinates would then be as follows:

( Xi ( ! A i ) fw = ( yi ( AAj ) fw ( (AAi) yc ( ( A Ai )

where fw = weighting factor, xi = distance from "y" axis to area section, yi = distance from "x" axis to area section, and AAj= incremental area section.

As with the basic centroid method, this method is often done by "eyeball" by an experienced fire investigator. However, the method also lends itself to more sophisticated computational analysis. In fact, there are several inexpensive computer-assisted drafting and design (CADD) programs available that will allow the building plan to be laid out on a computer screen and the fire-damaged areas drawn in as an overlay. Some of the CADD programs can then automatically find the centroid of an area.

It is also possible to scan in actual photographs of the fire scene and work directly from them in determining the point of origin, burn severity areas, etc. This, of course, requires that the photographs be taken from strategic vantage points. However, the use of actual photographs in conjunction with computer-generated overlays indicating the significance of the damage patterns visible in the photographs can be a very powerful demonstrative tool.

The "10" point system listed in Table 7.2 is somewhat arbitrary. Actually, any reasonable method of rating fire damaged areas can be used as long as the area of severest damage is assigned the highest weighting factor, and the area of least damage is assigned the lowest weighting factor. A simpler system using "1-2-3" is more practical for hand calculations. In that system, "3" is severe, "2" is moderate, "1" is light, and "0" is a no damage area.

One note of caution should be observed when using this method. Not all buildings burn homogeneously, of course. For example, if a fire had started in a kitchen and then spread to a storage area where an open 55 gallon drum of oil was stored, the most severely damaged fire area would be the storage

10 Materials are gone, wholly burned away

9 Materials are mostly gone, some residual

8 Materials are partially gone, recognizable residual

7 Materials are burned all over but shape intact

6 Materials are mostly burned

5 Materials are partially burned

4 Materials are slightly burned

3 Materials are heat damaged from nearby fire

2 Materials are heavily smoke damaged

1 Materials are slightly smoke damaged

0 Materials exhibit no significant fire damage

Table 7.2 Weighting Factors for Fire Severity

Factor

Description

Plate 7.3 Fire in garage that originated in dashboard short in the van. Note the greater fire damage on the right side of the roof.

area, not the kitchen. Thus, the initial reconnoiter of the damage should note where there were fuel concentrations that might skew the weighting.

0 0