NISTIR 7179 

Physics-Based Modeling for WUI 

Fire Spread – Simplified Model 

Algorithm for Ignition of 

Structures by Burning Vegetation 

David D. Evans 

Ronald G. Rehm 

Elisa S. Baker 

 

 

Supported in part by funds provided by 

Pacific Southwest Research Station 

Forest Service 

U.S. Department of Agriculture 
ii
NISTIR 7179 

Physics-Based Modeling for WUI 

Fire Spread – Simplified Model 

Algorithm for Ignition of 

Structures by Burning Vegetation 

David D. Evans 

Ronald G. Rehm 

Elisa S. Baker 

Fire Research Division 

Building and Fire Research Laboratory 

National Institute of Standards and Technology 

Gaithersburg, MD 20899 

October 2004 

U.S. Department of Commerce 

Donald L. Evans, Secretary 

Technology Administration 

Phillip J. Bond, Under Secretary for Technology 

National Institute of Standards and Technology 

Arden L. Bement, Jr., Director

U.S. Department of Agriculture 

Ann M. Veneman, Secretary 

Forest Service 

Dale N. Bosworth, Chief 

Pacific Southwest Research Station 

James Sedell, Director 
ii
iii

TABLE OF CONTENTS 

LIST OF FIGURES.................................................................................................................................... IV

LIST OF TABLES...................................................................................................................................... IV

1.0 ABSTRACT ........................................................................................................................................... 1

2.0 INTRODUCTION ................................................................................................................................. 1

3.0 BACKGROUND.................................................................................................................................... 2

3.1 PREVIOUS MODELING OF WILDLAND FUELS AND FIRES ............................................... 3

3.2 PREVIOUS MODELING OF WUI FIRES.................................................................................... 4

3.3 NIST RESEARCH CONTRIBUTION ............................................................................................ 4

4.0 BURNING CHARACTERISTICS OF DOUGLAS-FIR TREES ..................................................... 5 

 4.1 Experiments.......................................................................................................5 

4.1.1 Tree Preparation.......................................................................................................................... 5

4.1.2 Large Fire Laboratory................................................................................................................. 7

4.1.3 Instrumentation............................................................................................................................ 7

4.2 MEASUREMENTS ........................................................................................................................... 8

4.2.1 Flame Heights............................................................................................................................ 11

4.2.2 Heat Release Rate and Mass Loss ............................................................................................. 12

4.2.3 Other Measurements................................................................................................................. 13

4.3 ANALYSIS....................................................................................................................................... 13

4.3.1 Flame Height ............................................................................................................................ 13

4.3.2 Heat Release Rate ...................................................................................................................... 14

5.0 IGNITION OF STRUCTURES ALGORITHM FOR ECOSMART.............................................. 16

5.1 SIMPLE ALGORITHM FOR STRUCTURE IGNITION BY BURNING LANDSCAPE 

TREES.................................................................................................................................................... 17

5.1.1 Burnable Mass of the Tree ......................................................................................................... 18

5.1.2 Flame Height ............................................................................................................................ 18

5.1.3 Peak Heat Release Rate ............................................................................................................ 18

5.1.4 Radiative Fraction ..................................................................................................................... 19

5.1.5 Radiative Heat Flux ................................................................................................................... 19

5.1.6 Ignition Criteria ......................................................................................................................... 19

6.0 IMPLEMENTATION OF THE ALGORITHM IN ECOSMART .................................................. 19

7.0 MODELING COMPLEX PHENOMENA........................................................................................ 20

8.0 RESEARCH NEEDS TO ADVANCE THE DEVELOPMENT OF PHYSICS-BASED MODELS 

FOR WUI AND RESIDENTIAL HOUSING COMMUNITY FIRES................................................... 22

9.0 NIST FIRE DYNAMIC SIMULATOR AND SMOKEVIEW MODELS ..................................... 22

10.0 ACKNOWLEDGEMENTS ............................................................................................................... 23

11.0 REFERENCES ................................................................................................................................... 24

APPENDIX 

A............................................................................................................29ERROR! 

BOOKMARK NOT DEFINED.
iv

LIST OF FIGURES

Figure 1 Crown height ....................................................................................................... 6 

9Figure 2a. Pictures every 5 s of the Douglas-Fir-Tree Burns starting from the 

application of the igniter until 55 s after 

that....................................................................9 

Figure 2b. Pictures of the Douglas-Fir-Tree Burns for times between 60 s and 110 s after 

application of the igniter...........................................................................10 

10Figure 3 Flame height .................................................................................................. 11 

Figure 4 HRR as a function of time................................................................................. 12 

Figure 5 Flame height 

data........................................................................1313 

Figure 6 Heat release rate curves aligned at their peak values ........................................ 14 

Figure 7 Triangle approximation for the heat release rate of Douglas-fir crown fires ..... 15 

Figure 8 – Peak heat release rate from Douglas-fir trees as a function of moisture and 

mass........................................................................................................................... 16 

Figure 9 Three caricatures of a house representing different levels of complexity for 

mathematical models ............................................................................................... 21 

LIST OF TABLES 

Table 1 Douglas-fir tree identifications and physical measurements ................................ 7 

Table 2 Flame heights.................................................................................................. 1111 

Table 3 Measured peak heat release rate and burned weight loss for tree....................... 12 

Table 4 Tree height and flame height data....................................................................... 14 
Physics-Based Modeling for WUI Fire Spread – Simplified 

Model Algorithm for Ignition of Structures by Burning 

Vegetation 

David D. Evans, Ronald G. Rehm, and Elisa S. Baker 

Building and Fire Research Laboratory 

National Institute of Standards and Technology 

1.0 ABSTRACT 

A simple physics-based mathematical algorithm is described for estimating the separation 

distances necessary to prevent radiative ignition of structures by burning vegetation. The 

algorithm is directed at use in applications such as the USDA Forest Service EcoSmart 

software suite of tools. The algorithm represents a first step in quantifying the fire spread 

phenomena involving both structures and vegetation typical of wildland-urban interface 

(WUI) areas and residential housing communities. Results of initial experiments to 

characterize the heat release rate (HRR), flame height, and duration of burning for 

individual Douglas-fir trees are provided. In addition, research required to understand 

better and quantify wildland-urban and residential community fires are discussed. 

2.0 INTRODUCTION 

The Center for Urban Forest Research, the Pacific Southwest Research Center of the U.S. 

Department of Agriculture (USDA) Forest Service, together with other partners, is 

developing a web-based suite of software tools, called EcoSmart. EcoSmart is being 

developed for use by individual homeowners to provide guidance in assessing the 

contributions of landscape vegetation to home energy conservation, land hydrology, and 

fire spread. EcoSmart provides means to quantify the advantages and disadvantages of 

landscape vegetation relative to the costs. 

As a partner in this effort, with partial support from the Pacific Southwest Research 

Station, the Fire Research Division of the Building and Fire Research Laboratory of the 

National Institute of Standards and Technology (NIST) developed a simple physics-based 

mathematical model for estimating whether a structure will be ignited by nearby tree 

crown fires. This model quantifies the burning of vegetation in a manner that has not 

been done before. The model developed treats each tree, shrub, and house as an 

individual fuel element. In order to predict fire spread from burning fuel elements by 

ignition of other fuel elements, the ignition and burning characteristics of each fuel 

element and the interactions between elements has to be defined or determined. This 

creates a need for ignition and burning data that has not been generally measured before 

for vegetation and structures. With this data and appropriate models, the importance of 

individual fuel elements in fire propagation can be assessed. Resolving individual fuel 

elements in a model is necessary in order to properly evaluate the WUI and residential 
2

housing community fires. In these areas, structures are an important asset to be protected 

from fire, but can be an important source of fire spread if ignited. Fire spread in the WUI 

or residential housing communities cannot be characterized using the methods based on 

fuel bed classifications that are used widely to analyze the movement of fire fronts in 

forest fires. Regarding each structure as a fuel element, its likely fate in a fire can only be 

determined by examining its possible interactions with surrounding fuel elements that 

can, if burning, threaten the structure. The algorithm developed in this study is the first 

step in creating the foundation for a new method to analyze fire threat in WUI areas and 

residential communities. 

Version 1.0 of the fire algorithm developed by NIST is available for and compatible with 

the level of detail in other portions of the EcoSmart software under development. The 

algorithm documented in this report represents a first step in quantifying fire spread 

phenomena involving both structures and vegetation typical of wildland-urban areas and 

residential community properties. The report provides new data on HRR, flame height, 

and duration of burning for individual Douglas-fir trees. In addition, it also contains a 

discussion of research necessary to better understand and quantify wildland-urban and 

residential community fire spread. 

3.0 BACKGROUND 

The development of the EcoSmart suite of software tools began at the U.S. Department of 

Agriculture Forest Service, Pacific Southwest Research Station in 2002. There was a 

need to develop an algorithm that accounted for the increased risk for home destruction 

by fire due to the placement of trees and other ignitable vegetation close to the structure. 

This factor was in opposition to the benefits these plantings may have for energy 

conservation and soil hydrology. Development of the EcoSmart software suite of tools 

was undertaken to allow property owners to evaluate advantages and disadvantages, 

including fire safety and economics, of planting landscaping vegetation around homes. 

NIST was asked by the Pacific Southwest Research Station to develop a physics-based 

algorithm for ignition of structures by landscape vegetation that could be programmed 

into the EcoSmart suite of software tools and would be consistent with level of 

information and desired speed of operation of all the other parts of EcoSmart. Very little 

information was found in the literature that could be used to construct a physics-based 

model for ignition of structures by burning vegetation of the type and arrangement that 

would be present on landscaped properties. Principally, there was a lack of data on 

burning characteristics for individual trees and shrubs. 

Fire is an extremely complex natural phenomenon [1-10]. Decades of research to 

understand and quantify fire, together with revolutionary advances in computer 

technology and computational algorithms, have lead to the development of sophisticated 

mathematical models that can predict and visualize growth and spread of fire under a 

variety of conditions [11–16]. However, these models generally require substantial 

computational and data resources. Furthermore, since they have not been oriented toward 
3

the prediction of WUI or residential community fires, they will not soon be available for 

application by end users without a substantial research investment over the next few 

years. 

3.1 PREVIOUS MODELING OF WILDLAND FUELS AND FIRES 

Fires in the western U.S. have been headlines in the news for several recent years. 

Changes in the management of forested lands, the increasing intrusion of man into more 

remote areas and the cyclic dry periods produced by El Nino - La Nina have all increased 

the loss of man-made structures to fires. Wildland fires now often spread into the built 

environment causing injury, death and property damage. Concern about wildland fires 

and their effects on man and the built environment has generated increased interest 

recently, e.g., Livingston [17], Keller [18], Platt [19]. While the need to address fire 

spread in a mixed environment, containing both structures and wildland fuels, has been 

acknowledged, most research has continued to focus on wildland fires. Operational 

models that predict fire spread in wildland fuels are well developed and widely used, but 

do not yet address WUI fires. 

For over thirty years, modeling of fire dynamics in wildland fuels has been an ongoing 

research and development activity [20-26]. It has lead to practical or “operational” 

models that are regularly used by land managers to predict fire growth and spread for 

both planned or “controlled” burns and unexpected wildland fires. These operational 

models have served land managers and firefighters well both for planning controlled 

burns and suppression of wildfires. In the United States, the mathematical models 

BEHAVE [11] and FARSITE [12] are two of the most widely used operational models. 

Both are based upon the pioneering research of Rothermal [20, 21], who developed the 

framework for these models and determined many of the empirical relations used by it. In 

these models, wildland fuels are characterized by 13 standard fire behavior fuel types. 

These fuel characterizations and their behavior in wildland fires is the subject of several 

of the books cited above: Chandler et al [1], Chandler et al [2], Luke and McArthur [3], 

Pyne et al [4], and Brown and Davis [5] lists the 13 types and their characteristics. 

The basic model regards all of the fuel to cover the land surface as though it were 

“painted” on; i.e., all of the combustible material resides in fuel beds that have no vertical 

extent, but are strictly two dimensional. Fire then spreads over these fuel beds as a 

contour which divides unburned fuel from burned fuel or combustion products. Fuel beds 

can be homogeneous or inhomogeneous, isotropic or anisotropic, and they can be 

composed of a single fuel type or a combination of fuel types. Furthermore, the land 

surface may be flat or may have significant topographical features, and all of these 

variations make for differences in how the fire line progresses. 

Inclusion of improved descriptions of the physics in these models has progressed slowly 

in recent years and has not taken advantage of the revolution in computer hardware, and 

computational algorithms and software that has occurred over this same time frame. 
4

By comparison, over the past few decades, many of the physical and chemical processes 

occurring in fires have become much better understood, and physics-based mathematical 

and computational models have been developed to take advantage of this improved 

understanding. One such example is the work of Clark [27] and colleagues in which the 

coupling between large-scale wildland fires and the atmosphere has been studied. 

Another is modeling of the growth and spread of fires in structures, which has advanced 

dramatically using the methods of computational fluid dynamics (CFD) and, more 

generally, mathematical and computational methods that may be described as 

computational mechanics and computational combustion [28-31]. 

For models of combustion, the usual length scales of interest are measured in very small 

fractions of a meter (millimeters or less) to meters. Alternately, for problems related to 

computational mechanics or CFD, the length scales of interest can vary between meters 

and tens or even hundreds of meters. These scales should be contrasted with models for 

wildland fires, where the lengths are measured in kilometers or even hundreds of 

kilometers. 

3.2 PREVIOUS MODELING OF WUI FIRES 

Very little progress has been made on understanding and predicting fire spread at the 

Wildland-Urban Interface (WUI), where both wildland fuels and man-made structures 

coexist. At the WUI, the length scales are intermediate to the wildland scales on the one 

hand and to those associated with individual structures on the other. As a result, a model 

for a WUI fire must describe individual structures and trees in some detail, and must be 

able to determine fire spread between these individual fuel sources, a much more 

challenging task! One of the few studies to attack this very difficult problem is the work 

of Maranghides [32], who concluded that there was an extreme lack of relevant data. 

J. D. Cohen [33, 34] advocates the concept of a Home Ignition Zone, defined as the home 

and its surrounding area where heat transfer by radiation and/or convection from burning 

vegetation can ignite it. He is developing a model called the Structure Ignition 

Assessment Model (SIAM) to quantify this concept, which is being recognized as 

relevant to homeowners and firefighters. The model estimates conditions for home 

ignition. Once a home ignites in the calculation, it is considered lost. SIAM does not 

address the contribution of the burning structure to subsequent fire spread in the area. It 

therefore has limited application in the WUI, especially in cases of housing 

developments, where homes may be located within the Home Ignition Zone of its 

neighbors. 

3.3 NIST RESEARCH CONTRIBUTION 

In order to understand better the burning of landscape trees, a series of burns was 

performed in the NIST large fire facility to measure the burning characteristics of 

individual Douglas-fir trees. The measured burning characteristics of the trees were used 
5

as a basis for the construction of the algorithm for ignition of structures by burning 

vegetation. 

During this research, three papers were prepared that provide background and discussion 

of fire spread in the wildland-urban interface and in residential housing communities [35-

37]. In recent WUI fire disasters, visual evidence suggests that fully involved burning 

houses contribute to fire spread and destruction. Examples are given to show that the 

long-duration and high-intensity burning of a structure can contribute to altering the firegenerated winds [36]. In addition, early implementations of the structure ignition 

algorithm in EcoSmart are illustrated [35]. 

4.0 BURNING CHARACTERISTICS OF DOUGLAS-FIR TREES 

Although landscaping trees and shrubs, if ignited, can endanger near-by structures, very 

little quantitative information exists about ignition and burning characteristics of 

landscape vegetation. Generally, experiments carried out to measure the HRR of trees 

have been conducted to assess the hazards of Christmas tree fires [38-40]. No 

information has been found to quantify how the HRR, burn duration, and flame height 

vary with the size of a tree or tree species. Two studies were found in which the burning 

characteristics of shrubs were measured [41, 42]. 

Previously, the HRR of dry Scotch Pine trees was measured using the instrumented hood 

in the Large Fire Laboratory at NIST [38]. However, the study included only one size 

tree. The same is true for the study of Douglas-fir tree burning carried out by Babrauskas 

[39]. To take advantage of existing data, in this study we continued to burn cut Douglasfir trees. Three different commercial sizes were selected for the experiments. The height 

of the trees was limited by the HRR capacity of the Large Fire Laboratory exhaust hood. 

The tree burns provided important data for the algorithm development. Further 

experiments are needed to fully understand the burning characteristics. Data obtained 

from the burns provided information for the development of the algorithm that was not 

available from any other source. 

4.1 EXPERIMENTS 

Prior to burning, the cut trees were allowed to dry for 17 days as discussed below. All 

tree burns were conducted during a single week in the Large Fire Laboratory. This 

included time needed for instrument set-up and mounting each tree for burning. During 

each burn, the HRR, mass loss, flame height, vertical temperature profiles and radiant 

heat flux emitted from the fire were measured. 

4.1.1 Tree Preparation 

The Douglas-fir trees were purchased from a local nursery that grows Christmas trees. 

Three trees each with commercial sale heights of 1.2 m, 2.4 m, and 3.7 m (4 ft, 8 ft, and 

12 ft) were cut on July 6, 2003. These trees were delivered to NIST the following day 

and weighed. As the trees are a large fuel load, for fire safety considerations, the trees 
6

were dried on racks outside the Large Fire Laboratory. The racks were covered by tarps 

to shield the trees from rain. After 10 days, the trees were brought inside and weighed 

again to monitor the moisture lost to evaporation. Some of the trees had the base of the 

trunks trimmed to create a flat base for mounting on a stand that supported the tree 

upright for burning. 

The trees were photographed and heights were measured (see Table 1). The crown 

height is the height from the bole (height of the first live branches) to the top branch as 

shown in Figure 1. This differs from the commercial height of the tree which is 

measured from the base to the tip of the stem. The crown height best represents the 

burnable fuel height by eliminating the top of the stem and base of the tree up to the bole 

height. The stem needle growth on the test Douglas-fir trees that was eliminated from the 

burnable mass by this definition extend 0.3 m above the highest branch in some cases, 

but only added a small amount to the burnable fuel mass. 

 Figure 1 Crown height 
7

Tree Test No. Crown 

Height 

(m) 

Bole 

Height 

(m) 

Total 

Height 

(m) 

Weight 

7/7/03 

(kg) 

Weight 

7/17/03 

(kg) 

Weight 

Pre-burn 

(kg) 

Weight 

Pre-burn

Initial 

(7/7/03) 

4-1 Test 1 1.37 0.08 1.45 5.16 3.014 2.85 0.55 

4-2 Test 4 1.30 0.19 1.49 3.54 1.607 1.549 0.44 

4-3 Test 7 1.42 0.22 1.64 8.4 4.515 4.372 0.52 

8-1 Test 2 2.31 0.27 2.58 23.11 17.597 17.597 0.76 

8-2 Test 5 2.62 0.43 3.05 24.4 18.103 17.637 0.72 

8-3 Test 8 2.44 0.48 2.92 40.83 29.61 28.751 0.70 

12-1 Test 3 3.10 0.69 3.78 38.17 30.116 29.92 0.78 

12-2 Test 9 3.20 0.71 3.91 41.26 33.08 31.92 0.77 

12-3 Test 6 3.33 0.50 3.82 38.34 29.345 29.14 0.76 

Table 1 Douglas-fir tree identifications and physical measurements 

4.1.2 Large Fire Laboratory 

 

The trees were burned in the NIST Large Fire Laboratory located on the NIST site in 

Gaithersburg, Maryland. The facility has several instrumented hoods that employ oxygen 

consumption calorimetry to measure the HRR. The largest calorimeter hood, which was 

used for the tree burns, has a design capacity for HRRs of 10000 kW. The hood 

measures 9 m x 12 m and the lower edge of the hood is 4.5 m above the floor level. At 

its highest, in the center of the hood, the clear space above the floor is 7.9 m. The 

products of combustion are collected by the hood and flow though ducts for measurement 

and then are exhausted from the test building. After leaving the building the fire products 

are treated by a pollution abatement system before being discharged into the atmosphere. 

4.1.3 Instrumentation

The experiments were video taped from three different perspectives, and still digital 

photographs were also taken. The tree and stand were on a platform supported by a load 

cell that measured the mass loss as a function of time. Additionally, a much larger 

platform underneath the first was supported by load cells at each of the four corners, to 

verify the accuracy of the first load cell, and serve as a backup. 

Additional instrumentation included the following: 

Seven thermocouples were mounted on a 4.3 m (14 ft) vertical thermocouple support 

stand placed approximately a meter from each test tree. These thermocouples were 

mounted on horizontal arms at 0.61 m (2 ft) intervals, so that the sensing tips would be 

near the centerline of the tree crown in the buoyant gas nearest to the stem. The 

thermocouples were 3 mm diameter stainless steel sheathed, Type K Chomel-Alumel, 

0.91 m (3 ft) long. Voltage output from the thermocouple array was recorded on the 

Large Fire Laboratory data acquisition system. 

The first three tests had 4 water-cooled total-heat-flux gauges, which were mounted on a 

second 4.3 m (14 ft) vertical support located 3 m (9.8 ft) from the stem of the tree. The 

first gauge was located 0.61 m (2 ft) above the ground level, and the remaining three 
8

gauges were spaced vertically every 1.22 m (4 ft). Additionally, two heat flux gauges 

were placed aiming upward at ground level 1.5 m (4.9 ft) and 3 m (9.8 ft) from the tree 

stem. For the fourth through ninth tests, a seventh heat flux gauge was added, 10 m (32.8 

ft) away from tree stem. This gauge was angled at 20° to view the entire flame. 

4.2 MEASUREMENTS 

Figure 2 presents a timeline of images from the video record of all Douglas-fir tree burns 

except Test 9 (tree 12-2) that was lost. Each tree was ignited at the base of the crown 

using a propane torch with two flames for simultaneous ignition of the crown on opposite 

sides of the stem. Depending on the moisture content, some trees required 5 s of 

torch application to ignite, others required 15 s. Once ignited, each tree was consumed 

by rapid burning in approximately 60 s. 

All trees except Tree 12-1 behaved similarly in the burn tests. Tree 12-1 (Test 3) did not 

get fully involved, and required a re-ignition to sustain burning. Because of this unusual 

burning behavior the results for Test 3 are not included in the analysis. As there were 

two other trees of the same nominal size remaining in the data set, eliminating Test 3 

from the analysis was regarded as not significant. 
9

Figure 2a. Pictures every 5 s of the Douglas-Fir-Tree Burns starting from the application 

of the igniter until 55 s after that.
10

Figure 2b. Pictures of the Douglas-Fir-Tree Burns for times between 60 s and 110 s after 

application of the igniter. 
11

4.2.1 Flame Heights 

The mean flame height, Hflame was determined for each tree burn by analyzing video and 

still photos showing both the burning tree and the installed thermocouple supports. The 

flame height (see figure 3) was chosen to be the distance from the base of the flame near 

the tree bole (the lowest branch on the tree) to the top of the flame where the 

intermittency is 0.5. A flame intermittency of 0.5 means the visible flame is seen half of 

the time. For each burn, still photographs were used to determine the flame height, 

guided by the video record showing flame intermittency. The crown height, flame height 

and their ratio for each burn are shown in Table 2, and their use in the tree-burn model is 

presented in Sections 4.3.1 and 5.1.2. 

 Figure 3 Flame height 

Tree Hcrown (m) Hflame (m) Hflame /Hcrown

4-1 1.37 4.2 3.06 

4-2 1.30 3.47 2.68 

4-3 1.42 4.36 3.07 

8-1 2.31 4.61 1.99 

8-2 2.62 5.05 1.93 

8-3 2.44 5.61 2.30 

12-1 3.10 N/A N/A 

12-2 3.20 5.08 1.59 

12-3 3.33 4.69 1.41 

Table 2 Flame heights 
12

4.2.2 Heat Release Rate and Mass Loss 

Figure 4 shows a plot of the measured HRR for each of the tree-burns. The peak HRR 

occurs at different times in part because of variation in ignition times. Peak HRR and 

weight loss measured during the test are recorded in Table 3. The weight loss data in 

Table 3 are from the measurements made by the top load cell located directly under the 

tree. 

0

1000

2000

3000

4000

5000

6000

0 30 60 90 120

time (s)

HRR (kW)

12-3

12-2

8-3

8-2

8-1

4-3

4-2

4-1

Figure 4 HRR as a function of time 

Tree HRRpeak

(kW) 

Tree Weight 

Pre-burn 

(kg) 

Weight Loss 

(kg) 

Weight loss / 

pre-burn weight

4-1 780 2.85 1.44 0.51 

4-2 720 1.55 1.04 0.67 

4-3 1660 4.37 2.67 0.61 

8-1 3350 17.60 9.13 0.51 

8-2 3400 17.64 8.6 0.49 

8-3 5040 28.75 12.53 0.44 

12-2 5000 31.92 13.49 0.42 

12-3 4000 29.14 7.91 0.27 

Table 3 Measured peak HRR and burned weight loss for tree 
13

4.2.2 Other Measurements 

As part of the large scale experiments, many measurements, not needed immediately for 

the formulation of the algorithm, were recorded. These included temperature 

measurements from an array of thermocouples within and above the crown of the tree, 

and radiant and total heat flux from the fire at various distances and heights. These data 

will be reduced and analyzed when additional resources become available. 

4.3 ANALYSIS 

The series of tree-burn experiments provided initial data to start the formulation of the 

fire source portion of the algorithm to predict structural ignition from burning vegetation. 

Other observations from the data, not used directly in the development of the algorithm, 

are recorded in this section for possible use in other models for wildland-urban interface 

fires. 

4.3.1 Flame Height 

The mean flame heights (Hflame) were compared to the crown height, Hcrown, to determine 

if there was a correlation between a tree’s height, and the resulting flame height. The 

results are shown in figure 5. Generally the larger trees produced a flame height twice 

the crown height. The smallest trees produced a flame three times the crown height. This 

data is also influenced by differences in initial moisture content. From the data in Table 

1, the smallest trees lost about one-half of the initial weight before burning. The larger 

trees lost only one-fourth of the initial weight before burning. More experiments are 

needed to understand the effect of moisture and crown height on flame height. At this 

time, the best estimate of flame height for application to landscape trees is the data for the 

larger trees with greater moisture. That is Hflame / Hcrown = 2.0

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

H crown (m)

H flame / H crown

Figure 5 Flame height data 
14

Tree Hcrown (m) Hflame (m) Hflame/Hcrown

4-1 1.37 4.2 3.06

4-2 1.30 3.47 2.68

4-3 1.42 4.36 3.07

8-1 2.31 4.61 1.99

8-2 2.62 5.05 1.93

8-3 2.44 5.61 2.30

12-2 3.20 5.08 1.59

12-3 3.33 4.69 1.41

Table 4 Tree height and flame height data 

4.3.2 Heat Release Rate 

NIST tree burn experiments demonstrated that there is a similarity in the growth curves to 

peak HRR amongst all the trees, regardless of size. The heat release data from the 

experiments shows wide variation in the time to peak HRR (Figure 3). The larger trees 

took longer to ignite, and have a steeper rate of increase, but once the fire was steadily 

increasing, peak HRR was obtained in approximately 30 s for all trees. Figure 6 shows 

the HRR curves aligned such that the peak values occur at 30 s. From this figure, it is 

apparent that the size of the tree plays a large role in determining the peak HRR, but has a 

relatively minor affect on the length of the burn. 

Using 60 s as a common time interval for burning, the HRR of the burning Douglas-fir 

trees can be represented well by a simple isosceles triangle shape. In this case the base of 

the triangle is 60 s and the height is the peak HRR. Figure 7

HRR peaks

0

1000

2000

3000

4000

5000

0 10 20 30 40 50 60

delta t (s)

HRR (kW)

12-3

12-2

8-3

8-2

8-1

4-3

4-2

4-1

Figure 6 Heat release rate curves aligned at their peak values. 

shows this approximation as it applies to two of the measured HRR curves. This result is 

not used in the algorithm developed in this study, but may be an important and useful 

approximation in future modeling of crown fires. 
15

0

1000

2000

3000

4000

5000

0 10 20 30 40 50 60

time (s)

HRR (kW)

12-3

12-2

8-3

8-2

8-1

4-3

4-2

4-1

3.6 m

1.2 m

0

1000

2000

3000

4000

5000

0 10 20 30 40 50 60

time (s)

HRR (kW)

12-3

12-2

8-3

8-2

8-1

4-3

4-2

4-1

0

1000

2000

3000

4000

5000

0 10 20 30 40 50 60

time (s)

HRR (kW)

12-3

12-2

8-3

8-2

8-1

4-3

4-2

4-1

3.6 m

1.2 m

Figure 7 Triangle approximation for the heat release rate of Douglas-fir crown fires. 

The burning of Douglas-fir trees has also been studied to evaluate the hazards of 

Christmas trees in homes. In an extensive study of Christmas-tree burns by 

Babrauskas [39], peak HRR were correlated with total mass of the tree and the moisture 

content of the needles. A plot of the correlation and the curve-fit from the published 

results of that study are reproduced here as Figure 8 and Equation 1. .

peak q /mass = e

5.84-0.017M (1) 

Where, .

peak q is the peak heat release rate [kW], 

mass is the total pre-burn mass of the tree [kg], 

M is the moisture of the needles [mass fraction or percent by weight]. 

Because these results contain a quantification of the effect of moisture on the peak HRR 

and the trees burned were similar to those burned in this study, the results published by 

Babrauskas will be used in the formulation of the algorithm. As Babrauakas normalized 

his peak HRR using the entire mass of the cut Douglas-fir tree, his formulation will need 

to be modified to work with the burnable mass of the tree estimated from experiments 

conducted in this study. 
16

 

 Figure 8 – Peak heat release rate from Douglas-fir trees as a function of moisture 

and mass [39] (reproduced with permission from the Society of Fire 

Protection Engineers) 

5.0 IGNITION OF STRUCTURES ALGORITHM FOR ECOSMART 

In wildland-urban and residential community areas, fire can spread rapidly, often driven 

by wind, to threaten homes and other structures. There are several modes by which 

burning vegetation can threaten a home [1-8]. For example, flames from burning trees 

and shrubs close to a home can ignite combustible exteriors by direct contact. In addition, 

small fires in collected debris, such as dry leaves and needles dropped on and around the 

home, can start fires at corners and in small crevices of the structure. Furthermore, 

ground fires, which propagate in dead debris such as leaves or pine needles or in dry live 

fuels such as grasses, can ignite an exterior wall. All of these mechanisms depend 

essentially on direct contact (convection and/or conduction) for the heating and ignition 

of the combustible exterior materials of the structure. Alternately, hot brands from 

burning trees remote from the property can be carried by the wind and blown up-against 

the exterior or even into homes through small openings to ignite the structure. Or, finally, 

for large fires, thermal radiation emitted from the flames can be transported in line-ofsight directions across open spaces to be absorbed by and ignite the structure. 

Of these possible modes of fire spread, the most quantitative understanding exists for fire 

spread by ignition from thermal radiation [9, 10, 43-47]. For example, radiative heating 
17

of a surface is simply additive; therefore, the radiative heat flux at a position on the 

surface, from two identical non-interacting burning objects oriented similarly with 

respect to that position, is just twice that of one of them. In addition, radiation becomes a 

more dominant transport mechanism as fires become larger. Crown fires, which burn 

intensely and spread rapidly relative to other wildland fires, are well-known examples of 

fires where radiation is a dominant mode for fire spread. The fact that the heat transfer by 

radiation from burning trees to a structure could be quantified through knowledge of the 

geometric relationship between the two fuel elements, lead to the selection of this mode 

of ignition as to be the first to be quantified in EcoSmart [48-51]. This was done with 

full knowledge that more often structures are ignited by other means that are not well 

quantified as discussed above. A simple algorithm was constructed to determine the 

thermal radiation transport from trees to structures. 

The fire spread algorithm can be used to examine many scenarios for fire spread from 

vegetation to structures. The algorithm provides means to calculate the radiative heat 

exposure to structures from burning trees with flames located at arbitrary positions in 

3-dimensions relative to structural elements. 

Although it is well known that piloted radiative ignition of combustible materials depends 

on both the magnitude and the duration of the incident radiative heat flux [48-51], the 

model described here introduces only a simple critical flux assumption for ignition. To 

be consistent with other capabilities of the initial version of EcoSmart, the burning 

duration was eliminated from the algorithm for the ignition model. Fire spread from 

vegetation to the structure is assumed to occur, therefore, if the value of the radiative flux 

exceeds a critical value for ignition. In Section 5.1.6, there is additional discussion of this 

assumption, and a value of this critical flux. 

The computational relationships that form the basis for the initial fire spread model 

algorithm (version 1.0) for EcoSmart are summarized below. 

5.1 SIMPLE ALGORITHM FOR STRUCTURE IGNITION BY BURNING 

LANDSCAPE TREES 

The algorithm consists of six steps: 1) determine the burnable mass of the tree, 2) 

determine the flame height, 3) determine the peak HRR, 4) determine the fraction of the 

peak HRR emitted as radiative energy, 5) determine the fraction of the radiative flux 

emitted by the flame that impacts any part of the exterior surface, and 6) determine if the 

criteria for ignition of the exterior surface material is satisfied. The algorithm has been 

structured to utilize the burnable mass of the tree as a single parameter, to which burning 

properties are related. Future research may show that this single parameter can be used to 

generalize burning results between many different types of trees. As this study examined 

only one type of tree, however, experiments to determine additional data required for 

generalization of the results to other tree species, without generation of additional treeburn experiments, is not recommended. 
18

The measured mass loss during burning is used as the closest approximation to the 

burnable mass available for the trees burned in this study. The ratio of burnable mass for 

the trees to the pre-burn mass ranged from 0.27 to 0.65. 

5.1.1 Burnable Mass of the Tree 

The burnable mass of the tree is an input to the algorithm. This is often referred to as the 

foliar mass( mfoliar ) of the tree. This information is obtained from other sources within 

the EcoSmart software. 

 

5.1.2 Flame Height 

The flame height at peak burning rate is related to the crown height of the tree as shown 

in Figure 5. This data is complicated by the fact that both the size and the moisture 

content of the trees varied. More data is needed to understand the best way to relate 

flame height to the tree properties. For the algorithm, a fixed ratio of flame height to 

crown height equal to 2.0 is used. This choice is supported by the limited data. 

Therefore: 

Hflame = 2.0 Hcrown (2) 

where, 

Hflame [m], length of the flame above the bole of the tree, 

Hcrown [m], vertical distance from the bole to the highest branch. 

5.1.3 Peak Heat Release Rate 

The peak HRR is well known to be strongly dependent on the moisture content of the 

burnable mass. In a study of 2 m Douglas-fir tree burning conducted by Babraukas [39] 

the ratio of peak HRR decreases exponentially with increasing moisture content of the 

needles over the range in which the tree could be ignited. The correlation developed by 

Babraukas relates the peak HRR of the burning tree to weight of the tree at ignition. For 

an algorithm to be used in EcoSmart, the data must be presented in terms of burnable 

mass. In the Douglas-fir trees burns conducted in this study, the pre-ignition tree weight 

was approximately twice the mass loss during burning (see Table 3). As this fraction of 

the initial tree mass lost during burning is the best approximation to the burnable mass 

( mfoliar ) available from measurement made in this study, the correlation published by 

Babraukas has been multiplied by the factor 2 to adjust for use with the burnable mass 

parameter. The peak HRR for the algorithm is: 

M

peak foliar q m e5.84 0.017 .

2 − = (3) 

where 
19

.

peak q is the peak heat release rate [kW] 

mfoliar is the burnable mass of tree [kg] 

M is the moisture content of the needles [in percent of the needle mass] 

5.1.4 Radiative Fraction 

The fraction of heat emitted from a fire as thermal radiation can vary widely (see 

Quintiere [10]). Here, it is chosen to be a mid-range value of 0.35 (pp. 58-59 of reference 

[10] and HUD Report [52]). 

rad peak q q . .

= 0.35 (4) 

where, 

rad q

.

 [kW] is the peak emitted thermal radiation from the flame 

5.1.5 Radiative Heat Flux 

The heat flux at any part of the exterior surface of the structure is determined by a 

calculated view factor. The view factors are based on radiation from a vertical right 

cylinder body representing the flame orientated in 3-dimensions relative to the structure. 

The height of the cylinder is equal to the flame height (Hflame ), with the bottom of the 

cylinder position at the location of the bole of the tree. The calculation of view factors is 

given in Appendix A. 

5.1.6 Ignition Criterion 

The ignition criterion for the structure is based on a critical radiant flux condition. There 

is no dependence on exposure time. A single value of 31.5 kW/m2

 is used. This value is 

based on criteria developed by the Department of Housing and Urban Development for 

safe spacing of housing from potentially large fires [52, 53]. This value is relatively high 

compared to minimum heat flux values needed to ignite combustible exterior materials. 

However, without any time dependency for the ignition model in the algorithm and using 

only the peak radiant energy as exposure, this value is suitable for current use. 

6.0 IMPLEMENTATION OF THE ALGORITHM IN ECOSMART 

The fire model algorithm was selected to be physics-based and to harmonize as much as 

practical with the other modules of EcoSmart. Many choices that were made in the 

development of the algorithm for ignition of structures by burning vegetation were made 

specifically to work within the limitations of the EcoSmart software design. There is a 

greater quantitative understanding of fire spread from vegetation to structures than is 

implemented in the software. Full and detailed models of fire development on 

landscaped properties have been performed with the NIST developed Fire Dynamics 
20

Simulator (FDS) software [35-37]. Use of FDS directly in EcoSmart at this time is not 

practical because both the computational resources and the data requirements are too 

extensive. Using the algorithm developed where ignition of structures is based solely on 

fire radiant exposure should only be regarded as one indicator of fire spread potential 

from burning vegetation to structure. 

As already discussed, the initial structure-ignition algorithm for EcoSmart does not 

account for many well known fire spread mechanisms that threaten houses. For example, 

the model algorithm does not contain any effect of wind. It is well known that fire spread 

and spread rate are enhanced by wind, see for example Chapter 5 of Quintiere [10]. 

 Never-the-less as wind effects are not addressed in the first version of EcoSmart, they 

are not included in the structure-fire algorithm. Although many species of trees and 

shrubs will be available for use in the EcoSmart software, it was found that very little 

data is available that describes the burning of individual trees and shrubs in a form that is 

needed for the algorithm. As a result, new data was generated by NIST for burning 

Douglas-fir trees. As the vegetation burning portion of the algorithm was developed 

solely on data from Douglas-fir tree burns use of the Version 1.0 algorithm with other 

trees is not recommended. Additional research and data collection is needed to extend 

the algorithm to other tree species. 

As many potentially important fire spread mechanisms have been omitted, conservative 

choices that favored structure ignition have been made for the fire scenarios. This is 

customary practice in safety analysis where considerable uncertainties exist. In the 

algorithm: 

● All vegetation burns at the maximum burning rate. 

● All surfaces ignite if exposed to a critical flux for ignition. 

● Duration of burning for the sources of heat are not considered 

● Duration of exposure for the materials being ignited are not considered 

Since this version of EcoSmart has only implemented a model of structure ignition by 

thermal radiation, other important ignition threats to structures have been deferred for 

later development and implementation. For example, the initial version of the algorithm 

does not include the effects of ambient winds, burning brands and heat fluxes from 

nearby burning structures, for example. The determination of the relative importance of 

each of these effects is scenario dependent, and, therefore, inclusion of the effects will 

require additional research, data, and model development. 

7.0 MODELING COMPLEX PHENOMENA 

A mathematical model of any phenomenon can be regarded as a caricature of that 

phenomenon. By its very nature, modeling is a creative venture. Just as a caricature 

depends on the artist for its rendition, so mathematical modeling depends on the modeler 

for its mathematical description. If a model is well crafted and efficient, it will capture 
21

the important features of the phenomenon while ignoring less relevant ones and will 

produce results that are good representations of the phenomenon. 

Our ability to construct effective mathematical models depends on our understanding of 

the phenomenon. If, for example, we do not understand a phenomenon conceptually, we 

will not be able to develop a mathematical representation of it. As an aside, however, 

any attempt to construct a mathematical model often leads to a much better understanding 

of research needs by focusing attention on developing relationships between variables 

and data some of which may not be available. 

Mathematical models, even of the same phenomenon, can vary widely in complexity, as 

measured by several criteria: by the initial research and development effort required to 

construct the model, by the computational resources needed to use the model and by the 

data required for input and validation of the model. Using cost as the distinguishing 

feature, Figure 9 illustrates different classes of models by three caricatures of a house, 

ranging from most detailed on the left to the simplest on the right. We refer to the sketch 

on the left as a one-dollar model, the sketch on the right as a five cent model, and the 

center sketch as a 25 cent model. The price of each model is used here to convey the idea 

that greater model complexity generally leads to higher research and development costs, 

more extensive computer-resource requirements and greater data needs both for input and 

validation of the model. It also implies that greater model complexity usually yields a 

more faithful and easily understood representation of the phenomenon. 

Complexity is neither a reliable gauge of model accuracy nor effectiveness. The goal of 

any mathematical model is to produce the simplest representation of that phenomenon 

consistent with user needs to understand and predict its behavior. It is generally true that 

representing a complex phenomenon, like fire, requires a complex model (a dollar 

model). For example, a simple (five cent) model, while often adequate to illustrate may 

be inadequate or misleading for evaluations of details. 

 $1 25¢ 5¢ 

Complex Model: Approximate Model: 

Large Computational Small Computational 

and Data Needs and Data Needs 

Figure 9 Three caricatures of a house representing different levels of complexity for 

mathematical models. 
22

The mathematical model algorithm for ignition of structures used in version 1.0 of 

Ecosmart is distinctly a 5-cent class model. As noted earlier, many choices were made 

throughout the development of the algorithm to simplify the model in order to 

approximate the ignition potential of a structure due to nearby burning vegetation, while 

requiring minimal computer resources and minimal input/validation data. During a 

review of a pre-release version of the fire portion of the EcoSmart software, many of the 

model limitations were identified by the reviewers. These limitations have served as the 

starting point for defining research needs to improve future versions of the software. 

8.0 RESEARCH NEEDS TO ADVANCE THE DEVELOPMENT OF PHYSICSBASED MODELS FOR WUI AND RESIDENTIAL HOUSING COMMUNITY 

FIRES 

As discussed above, operational models are regularly used in practice by land-managers, 

and fire-prediction specialists, for example, to estimate the spread and spread rate of 

wildland fires. However, these models are limited, as noted above, and badly need 

updating to take into account of current mathematical modeling methodology and the 

revolutionary advances in computer technology over the past few decades. Since the 

wildland fuels simulated in the operational models have no vertical structure, the fire 

growth and spread are not governed by the conservation laws of physics. Therefore, there 

is no hope of generalizing these models to address the problem of fire spread to buildings, 

transitions from ground to crown fires, or fire spread from individual tree to tree. In other 

words, these models will never be able to model fires at the wildland-urban interface! 

When, in addition, the built environment becomes involved in a fire, as in the Oakland 

and Berkeley Hills fire of October 21, 1991, or more recently the Los Alamos fires in 

May 2000, Summerhaven, AZ, fires in June 2003, and San Diego, CA fires in OctoberNovember, 2003 these models are ineffective. The operational models cannot predict the 

spread of fire because the fuel load from buildings needs to be treated as discrete and 

three-dimensional. Also, in many cases the fuel load from structures is much larger than 

the surrounding vegetation. In order to model WUI and housing community fires, 

buildings, as well as large individual trees, must be regarded as discrete fuel elements on 

the length scales of interest. At a fundamental level, the empirical correlations upon 

which the wildland-fire operational models have been developed are no longer valid. 

Predictive methods are needed to address the potential fate of housing communities and 

individual high valued structures threatened by fire. No validated predictive models of 

fires in an urban or urban/wildland setting exist. Research is needed to develop threedimensional models of fire phenomena in WUI and housing communities. Measurement 

of three-dimensional burning characteristics of individual vegetation and man-made 

structure fuel elements are needed to support the model development. 

9.0 NIST FIRE DYNAMIC SIMULATOR AND SMOKEVIEW MODELS 

Over the past 25 years, the Building and Fire Research Laboratory (BFRL) at the 

National Institute of Standards and Technology (NIST) has developed a physics-based 

mathematical and computational model, known as the Fire Dynamics Simulator (FDS), to 
23

predict fire phenomena inside structures. Over time, this model has been used to predict 

outdoor buoyant plume behavior, outdoor fire spread from structure to structure, and, 

most recently, fire spread in both continuous and discrete wildland fuels. FDS, and a 

NIST-developed companion code for visualization called Smokeview have been well 

documented, validated using data from large-scale indoor and outdoor experiments, and 

are used by hundreds of fire protection engineers around the world. The model equations 

and their computational implementation in FDS have been carefully selected to be 

computationally efficient. Therefore, while FDS is both computationally and data 

intensive, simulations requiring on the order of a million or more computational cells 

generally require only a current high-end PC running overnight. Both codes and 

documentation can be downloaded free of cost from the URL: http://fire.nist.gov. 

The generation of mathematical models represented by FDS is based on the methodology 

of Computational Fluid Dynamics (CFD), and takes advantage of the revolutionary 

advances in computer technology with correspondingly reduced costs that make effective 

fire modeling capabilities widely available. There is a parallel between the current 

operational models for wildland fires and the previous generation of fire models 

developed by NIST in the 1980’s. These “zone-models” were effective in computing fire 

phenomena in structures, but only as average conditions on a room-by-room basis. The 

need for engineers to resolve greater details within rooms forced a transition to the 

present generation of FDS fire modeling. To advance fire modeling of WUI and 

residential communities, a new generation fire modeling tools must be developed for 

general use by land managers, community authorities, and property owners. 

At this time, there seems to be little to no research activity within the wildland-fire 

community directed at developing the next generation of three-dimensional fire models. 

NIST has begun to expand the capabilities of the FDS fire model and Smokeview fire 

visualization software to predict important fire phenomena occurring in the WUI and 

residential housing communities. This is a giant modeling undertaking. To estimate the 

order of magnitude of the research task to develop and validate a next-generation fire 

model, it has been estimated that NIST and its other agency partners have invested about 

100 scientific staff-years in the development of the present FDS and Smokeview tools! 

10.0 ACKNOWLEDGEMENTS 

The authors would like to thank Ms. Lisa Mabli for her enthusiastic support of this study 

with her insight into burning behavior and initial data on burning properties of vegetation. 

Initial data analysis and model development support was provided by Ms. Amaryllis 

Puig-Berrios. She served as a visiting scientist at NIST under the supervision of Dr. 

David Weiss from the Pacific Southwest Research Station. Development of new model 

representations for burning trees was contributed Dr. Sims Hostikka while at NIST as a 

visiting scientist from VTT in Finland. It was further refined by Dr. William Mell, 

formerly at the University of Utah, but now at NIST. Through the assistance of Mr. 

Alexander Maranghides and the operating technicians in the Large Fire Laboratory the 

tree burning experiments were conducted easily to produce the new data critical to the 

development of this model. Mr. Herbert Spitzer, Jr. contributed substantially in the 
24

review of the implementation of the algorithm in a pre-release version of EcoSmart. His 

comments were an initial guide to the research needs for further development of the WUI 

models. This research was funded in part by the Center for Urban Forest Research, 

Pacific Southwest Research Station, U.S. Department of Agriculture Forest Service. Dr. 

E. Gregory McPherson provided continued encouragement and coordination in the 

development of the algorithm. 

11.0 REFERENCES 

1. Chandler, Craig, Philip Cheney, Philip Thomas, Louis Trabaud and Dave Williams. 

1983. Fire in Forestry: Volume I Forest Fire Behavior and Effects, Wiley-Interscience, 

John Wiley and Sons, New York. 

 

2. Chandler, Craig, Philip Cheney, Philip Thomas, Louis Trabaud and Dave Williams. 

1983. Fire in Forestry: Volume II Forest Fire Management, Wiley-Interscience, John 

Wiley and Sons, New York. 

3. Luke, R. Harry and A.G. McArthur. 1978. Bushfires in Australia. Australian 

Government Publishing Service, Canberra. 

4. Pyne, Stephen J., Patricia L. Andrew and Richard D. Laven, , 1996. Introduction to 

Wildland Fire, second edition, John Wiley & Sons, Inc. New York. 

5. Brown, Arthur A. and Kenneth P. Davis. 1973. Forest Fire Control and Use, second 

edition, McGraw-Hill Book Company, New York. 

6. Johnson, E.A. and Miyanishi, M. (editors), Forest Fires, Behavior and Ecological 

Effects, Academic Press, San Diego, California. 2001. 

7. Albini, Frank A. 1984. Wildland Fires, American Scientist, 590-597. 

 

8. Pitts, W.M. 1991. Wind Effects on Fires. Prog. Energy Combust. Sci. 17:83-134. 

 

9. Drysdale, Dougal. 1985. An Introduction to Fire Dynamics, Wiley-Interscience 

Publications, John Wiley and Sons, New York. 

 

10. Quintiere, James G. 1998. Principles of Fire Behavior. Delmar Publishers, Albany, 

New York. 

 

11. Andrews, P.L., and C.D. Bevins. 1999. “BEHAVE Fire Modeling System: Redesign 

and Expansion. Fire Management Notes. 59:16-19; Web site: http://fire.org/. 

12. Finney, M.A. and P.L. Andrews, 1999. FARSITE - A Program for Fire Growth 

Simulation. Fire Management Notes. 59:13-15; Web site: http://fire.org/. 
25

13. McGrattan, K.B., H.R. Baum, R.G. Rehm, A. Hamins and G.P. Forney. 2000. Fire 

Dynamics Simulator - Technical Reference Manual. Nist Report NISTIR 6467, National 

Institute of Standards and Technology, Gaithersburg, Maryland. 

 

14. McGrattan, K.B. and G.P. Forney. 2000. Fire Dynamics Simulator -- User's Manual. 

Nist Report NISTIR 6469, National Institute of Standards and Technology, Gaithersburg, 

Maryland. 

15. Forney, G.P. and K.B. McGrattan. 2000. User's Guide for Smokeview Version 1.0 -- 

A Tool for Visualizing Fire Dynamics Simulation Data. NISTIR 6513, National Institute 

of Standards and Technology, Gaithersburg, Maryland.. 

16. Linn, R., J. Reisner, J. Colman, J. Winterkamp, 2002. Studying Wildfire Behavior 

using FIRETEK, International Journal of Wildland Fire, 11: 233-246. 

17. Livingston, R., Organizer, 2000. Second USGS Fire Science Workshop. Los Alamos, 

New Mexico. 

18. Keller, C., Organizer. 2000. Integrating Research on Wildland Fuels and Fires. Los 

Alamos, New Mexico. 

19. Platt, R., Roundtable Chair 200. Natural Disasters Roundtable, Forum on 

Urban/Wildland Fire. 26 January, National Academy of Sciences. Washington, D.C. 

20. Rothermel, Richard C. 1972. A Mathematical Model for Predicting Fire Spread in 

Wildland Fuels. USDA Forest Service Research Paper INT-115, Intermountain Forest 

and Range Experiment Station, Missoula Montana? Ogden Utah?. 

 

21. Rothermel, Richard C. 1983. How to Predict the Spread and Intensity of Forest and 

Range Fires. U.S. Intermountain Forest and Range Experiment Station, Ogden, Utah, 

Report PB 83-242289. 

22. Albini, Frank A. 1985. A Model for Fire Spread in Wildland Fuels by Radiation. 

Combust. Sci. and Tech. 42:229-258; also, Albini, Frank A. 1986. “Wildland Fire Spread 

by Radiation - A Model Including Fuel Cooling by Natural Convection,” Combust. Sci. 

and Tech. 45:101-113. 

 

23. Albini, Frank A. and Brian J. Stocks, “1986. Predicted and Observed Rates of Spread 

of Crown Fires in Immature Jack Pine,” Combust. Sci. and Tech. 48:65-76. 

 

24. Albini, Frank A. 1997. “An Overview of Research on Wildland Fire.” Proceedings of 

the Fifth International Symposium on Fire Safety Science, Yuji Hasemi, editor. 

 

25. Albini, F.A.. 1983. “Transport of Firebrands by Line Thermals,” Comb. Sci. & 

Tech.32:277-288. 

 
26

26. Albini, F.A.. 1981. Spot Fire Distance from Isolated Sources -- Extensions of a 

Predictive Model. Research Note INT-309, Dept. of Agriculture, Forest Service, 

Intermountain Forest and Range Experiment Station, Ogden Utah 

 

27. Clark, T.L., M.A. Jenkins, J. Coen and D. Packham. 1996. 

A Coupled Atmospheric-Fire Model: Convective Feedback on Fire-line 

Dynamics. J. Applied Meteorology 35:875-901. 

28. Baum, H.R., K.B. McGrattan and R.G. Rehm. 1994. “Simulation 

of Smoke Plumes from Large Oil Fires.” Twenty-Fifth Symposium 

(International) on Combustion, The Combustion Institute 25:1463-1469. 

29. Baum, H.R. 2000. “Large Eddy Simulations of Fire - from Concept to 

Computations.” Fire Protection Engineering 6:36-42. 

 

30. Baum, H.R. 2000. “Modeling and Scaling Laws for Large Fires.” Proceedings of 

ISSM-III, Third International Symposium on Scale Modeling, Nagoya, Japan. 

 

31. Baum, H.R., K.B. McGrattan and R.G. Rehm. 1994. “Mathematical Modeling and 

Computer Simulation of Fire Phenomena.” Theoretical and Computational Fluid 

Dynamics 6:125-139. 

 

32. Maranghides, A., 1993. Wildland-Urban Interface Fire Models, MS Thesis to 

Worchester Polytechnic Institute, December 8, 1993, 139pp. 

33 Cohen, J.D., 2000. Preventing Disasters, Home Ignitability in the Wildland-Urban 

Interface, Journal of Forestry, March 2000, pp15-21. 

34 Cohen, J.D. and Butler, B.W., 1996. “Modeling Potential Structure Ignitions from 

Flame Radiation Exposure with Implications for Wildland/Urban Interface Fire 

Management,” 13th Fire and Forest Meteorology Conference, Lorne Australia, pp. 81-86. 

35. Evans, D.D., R.G. Rehm, E.G. McPherson, Physics-based Modelling of WildlandUrban Intermix Fires, Proceedings, Third International Wildland Fire Conference, 

October 3-6, 2003, Sydney, Australia, 2003 

36. Rehm, R., D. Evans, W. Mell, S. Hostikka, K.McGrattan, G. Forney, C. Boulin, and 

E. Baker, Neighborhood-scale Fire Spread, Fifth Symposium on Fire and Forest 

Meteorology, 16-20 November, 2003, Orlando, Florida, 2003. 

37. Evans, D.D., Rehm, R.G., Baker, E.S., McPherson, E.G., Wallace, J.B., 2004, 

Physics-based Modeling of Community Fires, Proceedings 10th International Fire Science 

and Engineering Conference (Interflam 2004), 5-7 July, 2004, Edinburgh, Scotland, 

Interscience Communications Ltd, London, United Kingdom.
27

38. Stroup, D.W., L. DeLauter. J. Lee and G. Roadarmel. 1999. Scotch Pine Christmas 

Tree Fire Tests. NIST Report of Test FR 4010, National Institute of Standards and 

Technology, Gaithersburg, Maryland. 

39. Babrauskas, V., “Heat Release Rates”, The SFPE Handbook of Fire Protection 

Engineering (Third Edition), Section 3, Chapter 1, p 3-1, National Fire Protection 

Association, Quincy, Massachusetts 02269, 2002 

40. Damant, G. and S. Nurbakhsh, “Christmas Trees – What Happens When They 

Ignite?” Fire and Materials, 18, PP 916, 1994. 

41. Jennings, C.M., Development of Protocols for Testing the Exterior Components and 

Assemblies of Residential Structures Under Simulated Wildfire Conditions, MS Thesis in 

Wood Science and Technology, University of California, Forest Products Laboratory, 

Richmond, California, 2000. 

42. Etlinger, M.G., Fire Performance of Landscape Plants, MS Thesis in Wood Science 

and Technology, University of California, Santa Barbara, Santa Rosa Spring 2000. 

43. Hottel, H.C. and A.F. Sarofim, Radiative Transfer, 1967, McGraw-Hill Book 

Company, New York, New York. 

44. Siegel, R. and Howell, J.R., Thermal Radiation Heat Transfer, Third Edition, 

Hemisphere Publishing Corporation, Washington DC, Chapters 6 and 7. 

45. Howell, J.R., Website: http://www.me.utexas.edu/~Howell/ 

46.. Beyler, Craig L. (Task Group Chairman), Engineering Guide: Assessing Flame 

Radiation to External Targets from Pool Fires, The SFPE Task Group on Engineering 

Practices, June 1999 (FRIS R0000329) National Fire Protection Association, Quincy, 

Mass. 

47. Krishna S. Mudan and Paul A. Croce, Geometric View Factors, Fire Hazard 

Calculations for Large Open Hydrocarbon Fires, Section 2/Chapter 4, SFPE Handbook of 

Fire Protection Engineering, 2nd Edition; National Fire Protection Association, Quincy, 

Mass. 1995, p 2-57 to p 2-59. 

48. Cohen, J.D. and Butler, B.W., “Modeling Potential Structure Ignitions from Flame 

Radiation Exposure with Implications for Wildland/Urban Interface Fire Management,” 

13th Fire and Forest Meteorology Conference, Lorne Australia, 1996, pp. 81-86. 

49. Cohen, J.D., 2000. Preventing Disasters, Home Ignitability in the Wildland-Urban 

Interface, Journal of Forestry, PP 15-21, March 2000. 

50. Cohen, J.D., 2001. Wildland-urban fire--a different approach. In: Proceedings of the 

Firefighter Safety Summit, Nov. 6-8, 2001, Missoula, MT. Fairfax, VA: International 

Association of Wildland Fire. (www.umt.edu/ccesp/wfs/proceedings/Jack D. Cohen.doc) 
28

51. Cohen, J.D., “What is the Wldland Fire Threat to Homes,” The Thompson Memorial 

Lecture, April 10, 2000, School of Forestry, Northern Arizona University, Flagstaff, 

Arizona. 

52. Department of Housing and Urban Development. Siting of HUD-Assisted Projects 

near Hazardous Facilities – A Guidebook, Acceptable Separation Distances from 

Explosive and Flammable Hazards, September 1996, Department of Housing and Urban 

Development Report HUD-1060-CPD (1). 

53. Department of Housing and Urban Development, Safety Considerations in Siting 

Housing Projects, 1975, Housing and Urban Development Report 0050137. 

 
APPENDIX A

Model Geometry

Configuration Factor for the Cylindrical Flame of a Burning Conifer and an Element on the Target Structure.

The radiation exchange between individual elements (structures, trees, shrubs, etc.) at the Wildland-Urban Interface (WUI)

can be analyzed by the configuration-factor (CF) approach presented, for example, by Hottel and Sarofim [1] or by Siegel and

Howell [2], among others. Such an approach has been used by the Society of Fire Protection Engineers (SFPE) [3], [4] to assess

the thermal radiation to an external target from a pool fire. According to this analysis [3], three major steps are required:

1. Estimation of the characteristics of the pool fire, such as its radius, its flame height and its burning rate.

2. Estimation of the thermal radiation characteristics of the fire; e.g., its average emissive power, and

3. Calculation of the incident radiant flux at the target location.

Calculation of the incident radiant flux at a target structure can be accomplished by using the CF approach. In this approach,

the radiative exchange from an elemental area of the flame to an elemental area on the target is the fraction of the total energy

per unit time leaving the elemental flame area and incident upon elemental target area. This fraction depends upon the normal

angles of the emitting and the receiving surfaces and the distance between the two surfaces.

CF between a Finite-Length, Vertical Cylinder and a Differential Element on the Exterior of a Structure.

Figure 1: Schematic diagrams show the geometrical relationship between a finite-length, vertical circular cylinder, representation of a flame and a horizontal or a vertical elemental area at ground level.

Figure 1 shows a schematic diagram of a pool-fire flame modelled as a vertical, circular cylinder of height H and radius R.

The radiation from this model flame impinges on a vertical rectangular element at ground level at a horizontal distance L from

the axis of the cylindrical flame in the left diagram of Figure 1 and a horizontal rectangular element in the right diagram. The

Configuration Factor (CF), or the view factor, determines the fraction of the radiation from the flame that is incident on each

target element. F12,H is the CF for a horizontal target element and F12,V is the CF for a vertical element. Shokri and Beyler

[3] present analytical expressions for these Configuration Factors as functions of the two parameters, s, the dimensionless

horizontal distance of the target element from the centerline of the fire, and h, dimensionless cylindrical flame height:

s =

L

R

, h =

H

R

, A =

h

2 +s2 +1

2s

, B =

s

2 +1

2s

The CF for the horizontal element is

F12,H =

B−1/s

π

√

B2 −1

tan−1

s

(B+1)(s−1)

(B−1)(s+1)

−

A−1/s

π

√

A2 −1

tan−1

s

(A+1)(s−1)

(A−1)(s+1)

and the CF for the vertical element is

F12,V =

1

πs

tan−1



h

√

s

2 −1



−

h

πs

tan−1

s

(s−1)

(s+1)

+

Ah

πs

√

A2 −1

tan−1

s

(A+1)(s−1)

(A−1)(s+1)

29
CF between a model crown fire and a Differential Element on the Exterior of a Structure.

Now consider a crown fire in a single tree. As above, we will assume that flame can be modelled as a cylinder, and assume the top of the flame extends to height H above the ground, whereas the base of the flame is at the bole height, or the

height of the base of the crown D. NIST experiments show that the flame height extends from the base of the bole to twice

the crown height. Take the midpoint of the target element to be at height M above the ground and at a horizontal distance L

from the centerline of the flame. The Configuration Factors are pictured schematically in Figure 2 and can be determined by

the analytical expressions above of Shokri and Beyler [3] using techniques for addition of CFs [2].

Figure 2: Schematic diagrams showing a burning tree crown represented by a circular cylindrical flame

(color red) starting at height D, the base of the crown or the top of bole, and extending to height H.

NIST experiments show that the flame height extends from the base of the bole to twice the crown height. The Configuration Factor (CF) is calculated between the flame and differential vertical or horizontal elemental areas of height M

above ground level and at horizontal distance L from the centerline of the flame.

To model the CF between the crown fire and the vertical and horizontal elemental areas, we use the cylindrical-flame

analysis presented above. First, take a cylinder of height H −M :

s =

L

R

, h =

(H −M)

R

, A1 =

h

2 +s2 +1

2s

, B =

s

2 +1

2s

For this cylinder, the CF for the horizontal element is

F12a,H =

B−1/s

π

√

B2 −1

tan−1

s

(B+1)(s−1)

(B−1)(s+1)

−

A1 −1/s

π

q

A

2

1 −1

tan−1

s

(A1 +1)(s−1)

(A1 −1)(s+1)

and for the vertical element is

F12a,V =

1

πs

tan−1



h

√

s

2 −1



−

h

πs

tan−1

s

(s−1)

(s+1)

+

A1h

πs

q

A

2

1 −1

tan−1

s

(A1 +1)(s−1)

(A1 −1)(s+1)

Next, take a cylinder of height D−M :

s =

L

R

, d =

(D−M)

R

, A2 =

d

2 +s2 +1

2s

, B =

s

2 +1

2s

For this cylinder, the CF for the horizontal element is

F12b,H =

B−1/s

π

√

B2 −1

tan−1

s

(B+1)(s−1)

(B−1)(s+1)

−

A2 −1/s

π

q

A

2

2 −1

tan−1

s

(A2 +1)(s−1)

(A2 −1)(s+1)

30
and for the vertical element is

F12b,V =

1

πs

tan−1



d

√

s

2 −1



−

d

πs

tan−1

s

(s−1)

(s+1)

+

A2d

πs

q

A

2

2 −1

tan−1

s

(A2 +1)(s−1)

(A2 −1)(s+1)

The two CFs describing the crown fire should then be F12,H = F12a,H − F12b,H and F12,V = F12a,V − F12b,V . Written out fully,

then:

The CF from the crown fire to the horizontal element is

F12,H =

B−1/s

π

√

B2 −1

tan−1

s

(B+1)(s−1)

(B−1)(s+1)

−

A1 −1/s

π

q

A

2

1 −1

tan−1

s

(A1 +1)(s−1)

(A1 −1)(s+1)

−





B−1/s

π

√

B2 −1

tan−1

s

(B+1)(s−1)

(B−1)(s+1)

−

A2 −1/s

π

q

A

2

2 −1

tan−1

s

(A2 +1)(s−1)

(A2 −1)(s+1)





A2 −1/s

π

q

A

2

2 −1

tan−1

s

(A2 +1)(s−1)

(A2 −1)(s+1)

−

A1 −1/s

π

q

A

2

1 −1

tan−1

s

(A1 +1)(s−1)

(A1 −1)(s+1)

and for the vertical element is

F12a,V =

1

πs

tan−1



h

√

s

2 −1



−

h

πs

tan−1

s

(s−1)

(s+1)

+

A1h

πs

q

A

2

1 −1

tan−1

s

(A1 +1)(s−1)

(A1 −1)(s+1)

−





1

πs

tan−1



b

√

s

2 −1



−

b

πs

tan−1

s

(s−1)

(s+1)

+

A2b

πs

q

A

2

2 −1

tan−1

s

(A2 +1)(s−1)

(A2 −1)(s+1)





where, as before,

s =

L

R

, h =

(H −D)

R

, b =

(B−D)

R

A1 =

h

2 +s2 +1

2s

, A2 =

b

2 +s2 +1

2s

, B =

s

2 +1

2s

CF Dependence on Angles

The elemental area is regarded as part of the exterior wall of the target structure that is being irradiated by the cylindrical

crown-fire flame. There is a second plane which contains the axis of the cylindrical flame and is perpendicular to the irradiated

wall. This second plane contains lines perpendicular to the flame axis that determine the shortest distance between the flame

and the irradiated plane or wall. Figure 3 shows a schematic diagram of the ”flame,” the ”wall,” and the other geometrical

quantities discussed here.

In this geometry, the ”flame” model, the ”wall” and two angles define the CF. The first, θ1, is an elevation angle from

mid-height on the cylindrical flame surface to the center of the irradiated elemental area. This angle is in the vertical plane

containing the axis of the cylindrical flame, which is perpendicular to the plane of the elemental area (the second plane defined

above). This angle can be written as

θ1 = arctan

(D−M) +0.5(H −D)

L−R



= arctan

(d +0.5(h−d)

s−1



The second angle, θ2, is a lateral angle which is determined by the distance along the irradiated wall of the elemental area

from the normal plane (plane two above). If we define by X this lateral distance, and x as x = X/R, then this second angle θ2

can be written as

θ2 = arctan

X

L−R



= arctan

x

s−1



Including the effects of the angles on the configuration factor, we have

CFV = F12a,V cosθ1 cosθ2

31
Figure 3: Schematic diagram showing the geometry for a three-dimensional configuration factor

(CF) between a burning tree crown represented by a circular cylindrical flame (color red) starting at height D, the base of the crown or the top of the bole, and extending to height H.

NIST experiments show that the flame height extends from the base of the bole to twice the crown height. The Configuration Factor (CF) is calculated between the flame and the middle of a differential vertical element, which is of height 2

M.

or,

CFV /[cosθ1 cosθ2] = F12a,V

Finally, substitute for F12a,V :

CFV =





1

πs

tan−1



h

√

s

2 −1



−

h

πs

tan−1

s

(s−1)

(s+1)

+

A1h

πs

q

A

2

1 −1

tan−1

s

(A1 +1)(s−1)

(A1 −1)(s+1)



sinθ1 cosθ2

−





1

πs

tan−1



d

√

s

2 −1



−

d

πs

tan−1

s

(s−1)

(s+1)

+

A2d

πs

q

A

2

2 −1

tan−1

s

(A2 +1)(s−1)

(A2 −1)(s+1)



sinθ1 cosθ2

References

[1] Hottel, H.C. and A.F. Sarofim, Radiative Transfer, 1967, McGraw-Hill Book Company.

[2] Siegel, R. and Howell, J.R., Thermal Radiation Heat Transfer, Third Edition, Hemisphere Publishing Corporation, Washington, Chapters 6 and 7.

[3] Engineering Guide: Assessing Flame Radiation to External Targets from Pool Fires, The SFPE Task Group on Engineering Practices, Craig L. Beyler, Chairman, June 1999 (FRIS R0000329).

32
[4] Krishna S. Mudan and Paul A. Croce, Geometric View Factors, Fire Hazard Calculations for Large Open Hydrocarbon Fires, Section 2/Chapter 4, SFPE Handbook of Fire Protection Engineering, 2nd Edition; Natioinal Fire Protection

Association, Quincy, Mass. 1995, p2-57 to p2-59.

33