NIST Technical Note 2039

Measurement of the Flow Resistance of

Vegetation

Ryan Falkenstein-Smith

Kevin McGrattan

Blaza Toman

Marco Fernandez

This publication is available free of charge from:

https://doi.org/10.6028/NIST.TN.2039

NIST Technical Note 2039

Measurement of the Flow Resistance of

Vegetation

Ryan Falkenstein-Smith

Kevin McGrattan

Marco Fernandez

Fire Research Division

Engineering Laboratory

Blaza Toman

Statistical Engineering Division

Information Technology Laboratory

This publication is available free of charge from:

https://doi.org/10.6028/NIST.TN.2039

March 2019

U.S. Department of Commerce

Wilbur L. Ross, Jr., Secretary

National Institute of Standards and Technology

Walter Copan, NIST Director and Undersecretary of Commerce for Standards and Technology
Certain commercial entities, equipment, or materials may be identified in this document in order to describe

an experimental procedure or concept adequately. Such identification is not intended to imply

recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to

imply that the entities, materials, or equipment are necessarily the best available for the purpose.

The opinions, recommendations, findings, and conclusions in this publication do not necessarily reflect the

views or policies of NIST or the United States Government.

National Institute of Standards and Technology Technical Note 2039 

Natl. Inst. Stand. Technol. Tech. Note 2039, 34 pages (March 2019) 

CODEN: NTNOEF

This publication is available free of charge from: 

https://doi.org/10.6028/NIST.TN.2039
Abstract

This report documents the measurement of the wind resistance of different types of vegetation. The measurements are made in a wind tunnel with a 2.0 m test section and 0.5 m by

0.5 m cross-section. Samples of vegetation have been cut into cubical volumes that span

the cross-section of the tunnel. The wind resistance is inferred via measurement of the

pressure drop across the sample at wind speeds ranging from 2 m/s to 8 m/s. The results

are compared to empirical correlations quantifying the wind resistance of regularly spaced

vertical tubes of comparable geometric characteristics.

Key words

Vegetation Canopy; Drag Coefficient; Wind Resistance

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Table of Contents

1 Introduction 1

2 Model Development 1

3 Description of Experiments 4

3.1 Sample Preparation 4

3.2 Determining the Free-Area Coefficient via Photography 4

3.3 Description of the Wind Tunnel 4

3.4 Determining the Volume of Vegetation via Water Displacement 7

4 Results 10

4.1 Relationship between the Absorption Coefficient and Solid Fraction 10

4.2 Vegetation Canopy Drag Coefficients 11

5 Comparison Between Vegetation Data and Tube Bank Models 17

6 Conclusion 21

References 22

A Uncertainty Analysis of the Drag Coefficient 24

Appendix A: Uncertainty Analysis of the Drag Coefficient 24

A.1 Pressure 24

A.2 Air Density 24

A.3 Velocity 25

A.4 Free-Area Coefficient 25

B Uncertainty Analysis of the Absorption Coefficient 26

Appendix B: Uncertainty Analysis of the Absorption Coefficient 26

C Uncertainty Analysis of the Solid Fraction of Vegetation 27

Appendix C: Uncertainty Analysis of the Solid Fraction of Vegetation 27

C.1 Volume of Vegetation 27

C.2 Volume of Water Absorbed 27

C.3 Volume of Total Occupancy 27

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List of Tables

Table 1 Branch and leaf volume ratio of vegetation samples 10

Table 2 Drag coefficient summary of vegetation samples 16

Table 3 Parameters used in comparing vegetation with a comparable tube bank configuration 19

List of Figures

Fig. 1 Vegetation translation to multi-component model 2

Fig. 2 Cutting procedure of vegetation samples 5

Fig. 3 Prepared vegetation sample’s designated orientation 6

Fig. 4 Setup for photographing vegetation samples 7

Fig. 5 Wind tunnel experimental setup 8

Fig. 6 Procedure of the water displacement test 9

Fig. 7 Comparison of absorption coefficient, κ, and solid fraction, β 11

Fig. 8 Pressure drop versus velocity for all vegetative samples 12

Fig. 9 Determination of the drag coefficient for all vegetative samples 13

Fig. 10 Distribution of vegetation sample drag coefficients 14

Fig. 11 Tube bank experimental setup 18

Fig. 12 Comparison between resistance coefficients of tube banks 19

Fig. 13 Drag coefficient comparison between vegetation samples and tube bank configurations 20

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1. Introduction

The Fire Research Division of the National Institute of Standards and Technology (NIST)

has developed several numerical models to predict the behavior of fires within buildings.

One of the models, a computational fluid dynamics (CFD) code called the Fire Dynamics Simulator (FDS) [1], has been extended to model fires in the wildland-urban interface

(WUI). One crucial component of this type of modeling is the proper treatment of winddriven flow through vegetation. The objective of the experiments described in this report

is to measure the drag coefficient of vegetation for an empirical sub-model appropriate for

CFD.

Measurements of this type have been performed by other researchers [2–6], most of

whom used wind tunnels of various sizes. In most cases, a single plant or small tree was

positioned within the tunnel and the resistance force measured. However, such a measurement is not readily applicable to a CFD model which does not necessarily consider the tree

as a whole but rather as a volume occupied by subgrid-scale objects that decrease the momentum of the gases flowing through. Some plants might be smaller than a characteristic

grid cell, and some trees might be larger, but in either case, these objects are just momentum sinks within individual grid cells that require some drag coefficient that is appropriate

to the local conditions.

2. Model Development

Consider a volume filled with a random collection of vegetative elements, like pine needles

or leaves, as shown in Fig. 1. This volume can be regarded as a single grid cell in a CFD

model for which the computational domain may span hundreds to thousands of meters. At

a given instant in the numerical simulation, this grid cell would have, at the very least, an

average flow speed, U, and gas density, ρ. The vegetation within the cell is typically modeled as a collection of subgrid-scale Lagrangian particles whose mass, size, and shape are

characterized by a handful of parameters that can be determined with field measurements.

These particles exert a force per unit volume given by:

F =

N

Vc

ρ

2

Cd ApU

2

(1)

where N is the number of elements, Vc is the volume of the grid cell, Ap is the projected

area of a single element, and Cd is a drag coefficient. Similar configurations have already

been been adapted in numerical investigations [7, 8]. A more convenient way to describe

the vegetation is by specifying the surface to volume ratio of each element, σ, the volume

(packing) ratio of the collection of elements, β, and a shape factor, Cs, defined in this case

as the ratio of the element’s projected area to surface area. With this information, and the

following relations:

Cs =

Ap

As

; β =

NVe

Vc

; σ =

As

Ve

(2)

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Fig. 1. Vegetation translation to multi-component model

where Ve is the volume of an element and Asits surface area, we can convert the drag force

expression in Eq. (1) to an equivalent form [9]:

F =

ρ

2

CdCs β σ U

2

(3)

Some of the terms are difficult to measure, such as the shape factor and surface to volume

ratio, but collectively these terms may be combined into a single parameter:

κ = Cs β σ (4)

The parameter, κ, resembles an absorption coefficient1and can be determined by measuring the projected area of light, A, passing a given distance x through the vegetation. The

decrease in the projected area of light is governed by the equation

dA

dx

= −κ A ; A(x) = A(0) e

−κx

(5)

The relative fraction of light passing through a distance of L is

W =

A(L)

A(0)

= e

−κL

(6)

1Another way to express κ using the relations in Eq. (2) is NAp/Vc, or in other words, the total projected area

per unit volume. This parameter describes the absorption of non-scattering light by solid particles using the

same geometric assumption for thermal radiation absorption.

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The parameter W is sometimes referred to as the “free-area coefficient” or “free-area fraction” in the literature.

In order to measure the drag coefficient, Cd, a section of length, L, of a small wind

tunnel is to be filled with various amounts and types of vegetation and the pressure drop,

∆P, measured for an array of wind speeds, U. The value of κ shall be determined via black

and white photography, and the drag coefficient extracted from the following form of the

drag law derived above:

∆P

L

=

ρ

2

Cd κU

2

(7)

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3. Description of Experiments

3.1 Sample Preparation

The vegetation chosen for this work was a Bakers Blue Spruce (Picea pungens ‘Bakeri’), an

Evergreen Distylium (Distylium ‘PIIDIST-I’), a Gold Rider Leyland Cypress (Cupressocyparis leylandii ‘Gold Rider’), a Kimberly Queen Fern (Nephrolepis obliterata ‘Kimberly

Queen’), a Blue Shag Eastern White Pine (Pinus strobus ‘Blue Shag’), and a Robin Red

Holly (Ilex opaca). Each sample was chosen based on its local availability. Leaf shapes

were varied, including needle, elliptic, scale, and ovate.

The plant samples were cut into 0.5 m by 0.5 m by 0.5 m cubes using a guiding frame

(Fig. 2). The samples completely filled the cross section of the wind tunnel forcing the flow

to move through the vegetation as opposed to around it. To easily distinguish the front,

back, left, and right side of the cube-shaped vegetation, each side was designated Position

A, B, C, or D (Fig. 3). After its initial cut, image analysis, wind tunnel measurements,

and water displacement testing were conducted in subsequent order. Image analysis and

wind tunnel measurments were conducted for each position to obtain a collection of drag

coefficients relative to different κ values. In some cases, samples were pruned and tested

again. In the case of the Bakers Blue Spruce, Gold Rider Leyland Cypress, and Robin Red

Holly, four prunings were made with the final one being the removal of all leaves.

3.2 Determining the Free-Area Coefficient via Photography

The free-area coefficient, W, was determined by placing each vegetation sample on a table

located between a large white backdrop and a 0.5 m by 0.5 m cardboard frame, the same

dimensions as the tunnel cross section (Fig. 4). For each sample cut and position, the

projected area was photographed. All images were captured using a Nikon D5600 camera

placed on a tripod located approximately 3.6 m away from the sample. The white backdrop

was illuminated using a collection of incandescent and LED lights.

The images were processed using MATLAB’s Image Processing Toolbox. Imported

colored images were first converted into a grey scale and then a binary (black and white)

image using a pre-set threshold level. The binary images were then cropped within the

cardboard frame to eliminate non-vegetative substances and to evaluate the projected image

of the vegetation exclusively. Once the projected image was obtained, a pixel count was

conducted to determine the free-area coefficient of the vegetation, W. Once obtained, the

free-area coefficient was used to calculate κ from Eq. (6).

The uncertainty of the free-area coefficient, W, and the absorption coefficient, κ, are

discussed in Appendix A.4 and B, respectively .

3.3 Description of the Wind Tunnel

Pressure loss measurements were obtained in a wind tunnel test section with a crosssectional area of 0.5 m by 0.5 m and a length of 2 m. An image and schematic diagram of

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Fig. 2. Cutting procedure of vegetation samples

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Fig. 3. Prepared vegetation sample’s designated orientation

the wind tunnel setup is shown in Fig. 5. The volume flow through the tunnel was measured

upstream of the vegetation using a Rosemont 485 annubar [10]. The pressure drop across

the vegetation was measured using an MKS Baratron Type 220D pressure transducer with

a range of 0 to 133 Pa. The air flow was provided by a 0.91 m axial fan controlled by

a variable frequency drive and monitored using the Annubar. Air density was calculated

from pressure, temperature, and relative humidity readings of the testing facility. Each

sample configuration was subjected to nine different fan speeds ranging from 0 to 88 % of

the full-scale fan speed. The fan speed was not run at full scale due to the risk of exceeding

the pressure transducer’s pressure limitations. Data was sampled at 90 Hz for a 30 s period

while maintaining a constant fan speed.

Once a set of measurements was taken at all fan speeds, the wind tunnel was shut off for

approximately 5 min, and then the measurements were repeated. All measurements were

repeated three times for each vegetation configuration. The variance homogeneity of the

replicate measurements was tested using Hartley’s Fmax test. If it was found that the data

sets were homogenous, then the measurements were averaged.

An uncertainty analysis was conducted for the pressure and air density measurements

and the subsequently determined velocities and drag coefficients. The characterization of

the uncertainty for each parameter is provided in Appendix A.

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Fig. 4. Setup for photographing vegetation samples (left) and the post-processing procedure for

analyzing images (right)

3.4 Determining the Volume of Vegetation via Water Displacement

The volume of the vegetation was measured after a sample cut. The extracted vegetation

was separated into branches and leaves and put into cloth mesh bags of known mass and

volume, weighed2, and submerged in a bucket. The displaced water flowed through a spout

and into a beaker (Fig. 6). The measurement was repeated three times for each sample. The

solid fraction, β, was calculated by dividing the average sample volume by the volume it

occupied (0.5 m × 0.5 m × 0.5 m = 0.125 m3).

2The mass was measured to estimate the water absorbed by the sample in between tests. The volume of water

absorbed was subtracted from the volume of vegetation measured from the beaker.

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Fig. 5. Wind tunnel experimental setup with top and front schematic drawings

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Fig. 6. Procedure of the water displacement test

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4. Results

The key results of this work are the relationship between the absorption coefficient, κ, and

the solid fraction, β, and the drag coefficient derived from the wind tunnel measurements.

4.1 Relationship between the Absorption Coefficient and Solid Fraction

Figure 7 presents the relationship between the averaged absorption coefficient, κ, and the

solid fraction, β, for the sample configurations of the Bakers Blue Spruce, Evergreen Distylium, Gold Rider Leyland Cypress, and Robin Red Holly. The symbols indicate the measured values while the dotted lines represent a linear regression fit. Each line represents

a particular type of vegetation that has been pruned, reducing both the volume fraction,

β, the projected free-area coefficient, W, and the corresponding value of κ. There ought

to be a linear relationship between κ and β if the shape factor, Cs, and surface to volume

ratio, σ are constant, as shown in Eq. (4). However, this is not the case when the vegetative

components are not uniform in size. Take, for example, the Robin Red Holly data shown

in Fig. 7. As β decreases, κ should approach zero, as demonstrated by most samples. As

the leaves of the Robin Red Holly were pruned, κ decreased significantly even though its

volume fraction did not, owing to the fact the ratio of branch to leaf volume of the Robin

Red Holly is substantially higher than the other plant species, as shown in Table 1. As

a result, the free-surface area, W, decreases from the removal of leaves, thus reducing κ,

while still maintaining a relatively consistent solid fraction due to the significant volume

contribution of the branches.

Table 1. Branch and leaf volume ratio of vegetation samples with mulitple cut iterations

Sample β (%) Branch/Leaf Vol. Sample β (%) Branch/Leaf Vol.

Blue Spruce 1.9 1.1 Cypress 1.7 1.5

1.8 1.3 1.4 2.2

1.2 1.5 1.2 3.0

0.7 N/A 0.9 N/A

Distylium 0.5 1.0 Red Holly 2.7 11

0.4 1.4 2.3 16

0.3 3.3 2.2 47

2.1 N/A

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Fig. 7. Calculated absorption coefficient (κ) of vegetation sample configuration plotted against the

corresponding solid fractions (β)

4.2 Vegetation Canopy Drag Coefficients

Figure 8 displays the relationship between the freestream velocity and the pressure drop

for each sample configuration. The results demonstrate the expected quadratic relationship. Replotting the data as shown in Fig. 9 yields the drag coefficient for each sample

configuration as determined by calculating the slope of each line of data points. No linear regression fitting was observed to have a coefficient of determination less than 0.98,

indicating a close representation of the fitted regression line to the measured data. A summary of all 68 calculated drag coefficients and their respective uncertainties are presented

in Table 2

3

.

The distribution of the measured drag coefficients for all sample configurations is shown

3The procedure for determining the drag coefficient uncertainty as shown in this table can be found in Appendix A. For most instances, the uncertainty in the velocity measurement was found to be the primary

contributor to the drag coefficient uncertainty. In other cases, the uncertainty of the measured pressure loss

across the vegetation was the primary contributor to the drag coefficient uncertainty.

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0 2 4 6 8 10

0

80604020

140120100

Bakers Blue Spruce,Cut 0 (PA)Bakers Blue Spruce,Cut 0 (PB)Bakers Blue Spruce,Cut 0 (PC)Bakers Blue Spruce,Cut 0 (PD)Bakers Blue Spruce,Cut 1 (PA)Bakers Blue Spruce,Cut 1 (PB)Bakers Blue Spruce,Cut 1 (PC)Bakers Blue Spruce,Cut 1 (PD)Bakers Blue Spruce,Cut 2 (PA)Bakers Blue Spruce,Cut 2 (PB)Bakers Blue Spruce,Cut 2 (PC)Bakers Blue Spruce,Cut 2 (PD)Bakers Blue Spruce,Cut 3 (PA)Bakers Blue Spruce,Cut 3 (PB)Bakers Blue Spruce,Cut 3 (PC)Bakers Blue Spruce,Cut 3 (PD)Blue Shag Eastern White Pine,Cut 0 (PA)Blue Shag Eastern White Pine,Cut 0 (PB)Blue Shag Eastern White Pine,Cut 0 (PC)Blue Shag Eastern White Pine,Cut 0 (PD)Evergreen Distylium,Cut 0 (PA)Evergreen Distylium,Cut 0 (PB)Evergreen Distylium,Cut 0 (PC)Evergreen Distylium,Cut 0 (PD)Evergreen Distylium,Cut 1 (PA)Evergreen Distylium,Cut 1 (PB)Evergreen Distylium,Cut 1 (PC)Evergreen Distylium,Cut 1 (PD)Evergreen Distylium,Cut 2 (PA)Evergreen Distylium,Cut 2 (PB)Evergreen Distylium,Cut 2 (PC)Evergreen Distylium,Cut 2 (PD)Gold Rider Leyland Cypress,Cut 0 (PA)Gold Rider Leyland Cypress,Cut 0 (PB)

Gold Rider Leyland Cypress,Cut 0 (PC)Gold Rider Leyland Cypress,Cut 0 (PD)Gold Rider Leyland Cypress,Cut 1 (PA)Gold Rider Leyland Cypress,Cut 1 (PB)Gold Rider Leyland Cypress,Cut 1 (PC)Gold Rider Leyland Cypress,Cut 1 (PD)Gold Rider Leyland Cypress,Cut 2 (PA)Gold Rider Leyland Cypress,Cut 2 (PB)Gold Rider Leyland Cypress,Cut 2 (PC)Gold Rider Leyland Cypress,Cut 2 (PD)Gold Rider Leyland Cypress,Cut 3 (PA)Gold Rider Leyland Cypress,Cut 3 (PB)Gold Rider Leyland Cypress,Cut 3 (PC)Gold Rider Leyland Cypress,Cut 3 (PD)Kimberly Queen Fern,Cut 0 (PA)Kimberly Queen Fern,Cut 0 (PB)Kimberly Queen Fern,Cut 0 (PC)Kimberly Queen Fern,Cut 0 (PD)Robin Red Holly,Cut 0 (PA)Robin Red Holly,Cut 0 (PB)Robin Red Holly,Cut 0 (PC)Robin Red Holly,Cut 0 (PD)Robin Red Holly,Cut 1 (PA)Robin Red Holly,Cut 1 (PB)Robin Red Holly,Cut 1 (PC)Robin Red Holly,Cut 1 (PD)Robin Red Holly,Cut 2 (PA)Robin Red Holly,Cut 2 (PB)Robin Red Holly,Cut 2 (PC)Robin Red Holly,Cut 2 (PD)Robin Red Holly,Cut 3 (PA)Robin Red Holly,Cut 3 (PB)Robin Red Holly,Cut 3 (PC)Robin Red Holly,Cut 3 (PD)

Fig. 8. Measured pressure drop versus freestream velocity for all vegetative samples.

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0 10 20 30 40 50

0

80604020

180160140120100

Bakers Blue Spruce,Cut 0 (PA)Bakers Blue Spruce,Cut 0 (PB)Bakers Blue Spruce,Cut 0 (PC)Bakers Blue Spruce,Cut 0 (PD)Bakers Blue Spruce,Cut 1 (PA)Bakers Blue Spruce,Cut 1 (PB)Bakers Blue Spruce,Cut 1 (PC)Bakers Blue Spruce,Cut 1 (PD)Bakers Blue Spruce,Cut 2 (PA)Bakers Blue Spruce,Cut 2 (PB)Bakers Blue Spruce,Cut 2 (PC)Bakers Blue Spruce,Cut 2 (PD)Bakers Blue Spruce,Cut 3 (PA)Bakers Blue Spruce,Cut 3 (PB)Bakers Blue Spruce,Cut 3 (PC)Bakers Blue Spruce,Cut 3 (PD)Blue Shag Eastern White Pine,Cut 0 (PA)Blue Shag Eastern White Pine,Cut 0 (PB)Blue Shag Eastern White Pine,Cut 0 (PC)Blue Shag Eastern White Pine,Cut 0 (PD)Evergreen Distylium,Cut 0 (PA)Evergreen Distylium,Cut 0 (PB)Evergreen Distylium,Cut 0 (PC)Evergreen Distylium,Cut 0 (PD)Evergreen Distylium,Cut 1 (PA)Evergreen Distylium,Cut 1 (PB)Evergreen Distylium,Cut 1 (PC)Evergreen Distylium,Cut 1 (PD)Evergreen Distylium,Cut 2 (PA)Evergreen Distylium,Cut 2 (PB)Evergreen Distylium,Cut 2 (PC)Evergreen Distylium,Cut 2 (PD)Gold Rider Leyland Cypress,Cut 0 (PA)Gold Rider Leyland Cypress,Cut 0 (PB)

Gold Rider Leyland Cypress,Cut 0 (PC)Gold Rider Leyland Cypress,Cut 0 (PD)Gold Rider Leyland Cypress,Cut 1 (PA)Gold Rider Leyland Cypress,Cut 1 (PB)Gold Rider Leyland Cypress,Cut 1 (PC)Gold Rider Leyland Cypress,Cut 1 (PD)Gold Rider Leyland Cypress,Cut 2 (PA)Gold Rider Leyland Cypress,Cut 2 (PB)Gold Rider Leyland Cypress,Cut 2 (PC)Gold Rider Leyland Cypress,Cut 2 (PD)Gold Rider Leyland Cypress,Cut 3 (PA)Gold Rider Leyland Cypress,Cut 3 (PB)Gold Rider Leyland Cypress,Cut 3 (PC)Gold Rider Leyland Cypress,Cut 3 (PD)Kimberly Queen Fern,Cut 0 (PA)Kimberly Queen Fern,Cut 0 (PB)Kimberly Queen Fern,Cut 0 (PC)Kimberly Queen Fern,Cut 0 (PD)Robin Red Holly,Cut 0 (PA)Robin Red Holly,Cut 0 (PB)Robin Red Holly,Cut 0 (PC)Robin Red Holly,Cut 0 (PD)Robin Red Holly,Cut 1 (PA)Robin Red Holly,Cut 1 (PB)Robin Red Holly,Cut 1 (PC)Robin Red Holly,Cut 1 (PD)Robin Red Holly,Cut 2 (PA)Robin Red Holly,Cut 2 (PB)Robin Red Holly,Cut 2 (PC)Robin Red Holly,Cut 2 (PD)Robin Red Holly,Cut 3 (PA)Robin Red Holly,Cut 3 (PB)Robin Red Holly,Cut 3 (PC)Robin Red Holly,Cut 3 (PD)

Fig. 9. Determination of the drag coefficient for all vegetative samples.

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Fig. 10. Distribution of drag coefficients for all samples (top), samples with narrow leaves (bottom

left), samples with broad leaves (bottom right).

in Fig. 10. The collection of sample configurations is divided into two groups based on leaf

shape (i.e., narrow and broad). The narrow leaves group included the Bakers Blue Spruce,

Blue Shag Eastern White Pine, and Gold Rider Leyland Cypress while the broad leaves

group was comprised of the remaining species. The average drag coefficient of all sample

configurations was determined to be 2.8 with an expanded uncertainty of 0.4.

To determine if the average drag coefficient depends on the type of vegetation a random effects one-way ANOVA4 was implemented on the drag coefficients of the different vegetation samples. The analysis yielded a significant variation (F(5,62) = 4.88,

p = 7.97 × 10−4) among the species5. A Tukey’s test [11] was subsequently applied to

determine if the species-specific average drag coefficients were significantly different from

4Analysis of Variance

5The F refers to the statistic obtained from the F-test conducted in the ANOVA, the 5 and 62 in brackets

represent the degrees of freedom, and the 4.88 is the actual F statistic derived from the ANOVA. The p

refers to the significance level determined from the F statistic and the 7.97 × 10−4is the actual p-value

which was determined to be less than the chosen confidence level of 0.05, indicating a significant difference

between the mean drag coefficients of the samples.

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each other. The results showed one significant difference between the species’ average drag

coefficients: the Robin Red Holly and Gold-Rider Leyland Cypress. Despite the significant difference, the average drag coefficients of these two plant species are still within the

uncertainty bound of the overall drag coefficient and therefore are not large enough to have

a practical implication.

Further analysis was conducted to compare the two leaf shape groups. A one-way

random effects model [12] for the measurements of the narrow leaves group assumes that

the drag coefficients are normally distributed:

Cd,i j ∼ N(m1,ui j

2 +σ12

), i = 1,...,3; j = 1,...,ni (8)

where i denotes the plant species (1 for Bakers Blue Spruce, 2 for Blue Shag Eastern White

Pine, and 3 for Gold Rider Leyland Cypress), and j denotes the specific configuration of

the plant in the tunnel. The sample size for a given plant species is ni. The value of

ui j is the standard uncertainty of the measured drag coefficient for a specific species and

configuration. The parameters m1 and σ1 are the mean and standard deviation for the

narrow leaves group, respectively. The drag measurements of the broad leaves group are

modeled in a similar way:

Cd,i j ∼ N(m2,ui j

2 +σ22

), i = 4,...,6; j = 1,...,ni (9)

where i = 4 for Distylium, i = 5 for Fern, and i = 6 for Red Holly). The parameters m2 and

σ2 are the mean and standard deviation for the broad leaves group, respectively.

Using a Bayesian statistical model [13] with non-informative priors for m1, m2, σ1,

and σ2, we obtain via Markov Chain Monte Carlo implemented in OpenBUGS [14] the

posterior means and standard uncertainties of the parameters. These are: m1 is 3.0 with an

expanded (95 %) uncertainty of 0.3, m2 is 2.5 with an expanded (95 %) uncertainty of 0.3,

and the 95 % uncertainty interval for the difference m1 −m2 is (0.052, 0.87). This may be

interpreted as a rejection of a hypothesis test of H0: m1 −m2= 0 at a level of 5 %. Despite

the differences in the average drag coefficients of both groups, they both lie within the

uncertainty bound of the overall average drag coefficient, which suggests that mean drag

coefficient obtained from all samples could be a reasonable approximation when applied

as a consistent drag coefficient for vegetation canopies in CFD models.

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Table 2. Drag coefficient summary of vegetation samples

Sample β (%) Position Cd Uncertainty Sample β (%) Position Cd Uncertainty

Blue Spruce 1.9 A 3.6 0.5 Cypress 1.7 A 3.0 0.5

B 3.1 0.5 B 3.2 0.5

C 3.1 0.4 C 3.4 0.5

D 3.0 0.4 D 3.0 0.4

1.8 A 3.8 0.5 1.4 A 3.3 0.4

B 3.0 0.4 B 2.9 0.4

C 3.1 0.4 C 3.3 0.4

D 3.6 0.4 D 3.8 0.4

1.2 A 3.2 0.4 1.2 A 2.1 0.5

B 2.6 0.3 B 3.2 0.3

C 2.5 0.3 C 3.1 0.4

D 2.8 0.3 D 3.3 0.4

0.7 A 2.5 0.4 0.9 A 2.9 0.4

B 2.3 0.4 B 3.9 0.4

C 2.2 0.4 C 3.0 0.5

D 2.2 0.4 D 3.8 0.5

White Pine 2.8 A 4.4 0.7 Fern 0.4 A 3.4 0.5

B 2.8 0.4 B 3.1 0.4

C 2.1 0.4 C 3.3 0.5

D 3.6 0.5 D 2.6 0.4

Distylium 0.5 A 3.2 0.4 Red Holly 2.7 A 3.1 0.5

B 2.9 0.4 B 2.6 0.4

C 3.1 0.4 C 2.5 0.4

D 3.4 0.4 D 2.7 0.4

0.4 A 2.7 0.3 2.3 A 2.8 0.4

B 2.3 0.3 B 2.0 0.3

C 3.1 0.4 C 2.5 0.3

D 2.9 0.4 D 1.8 0.3

0.3 A 2.0 0.3 2.2 A 3.4 0.3

B 1.5 0.2 B 2.2 0.2

C 1.7 0.3 C 2.7 0.3

D 2.6 0.3 D 2.5 0.3

2.1 A 2.1 0.3

B 1.6 0.3

C 1.6 0.3

D 1.7 0.3

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5. Comparison Between Vegetation Data and Tube Bank Models

In comparison to previous work [2–6], the magnitude of the measured drag coefficients

in this study is relatively large. As discussed in Section 1, most previous studies have

measured the wind resistance of a single plant or tree within a larger wind tunnel while this

work considered a relatively homogenous distribution of vegetation within a tunnel. The

interpretation of “freestream” velocity, shape factor, cross-sectional area, and so on, are

often different in these studies, making it difficult to compare drag coefficients from one

study to another. Within the field, there is no single definition of drag coefficient regarding

vegetation.

As a way to verify the accuracy of our wind tunnel measurements and the validity of

our drag coefficient derivation, we considered a bank of regularly-spaced vertical cylinders

within our wind tunnel, using both actual steel rods and empirical results from Idelchik [15].

The pressure loss across two rows of six in-line 2.5 cm stainless steel cylinders was measured using the experimental setup described in Section 3.3 and shown in Fig. 11. The “resistance coefficient” (termed by Idelchik) for tube banks was calculated from the measurements and the empirical model. Figure 12 shows that the measured resistance coefficient is

within experimental uncertainty of Idelchik’s empirical model, verifying our experimental

approach.

Furthermore, for each of the measured vegetation samples, a comparable configuration

of vertical tubes was chosen such that the volume fraction, β, absorption coefficient, κ, and

characteristic diameter, D, match as closely as possible (see Table 3). The characteristic

diameter was calculated from Eq. (4) using the measured β and κ values and assuming a

cylindrical shape factor (Cs = 1/π). To account for the repeated tube formation for each

row, the κ value of the tube bank was determined from the distance between rows, L

0

,

and Eq. (6). Although the length parameter is modified, the control volume definition of

the product of the cross-section of the tunnel and depth of the blockage still holds true.

According to Idelchik, the expected pressure drop through the tube bank is:

∆P =

ρ

2

ζ



U

W

2

; ζ = ARe−0.27(Nr +1) ; Re =

(U/W)Dρ

μair

(10)

where A is a geometric parameter determined from the tube bank configuration, Nris the

number of rows of tubes, W is the free-area fraction, U/W is the average velocity of air

flowing through the tube array, and Re is the Reynolds number which must be greater than

3000 for the empirical model to apply. Setting the pressure drop, ∆P, in Eq. (10) equal to

that in Eq. (7) leads to an equivalent drag coefficient for the tube bank:

Cd =

ζ /W2

κ L

(11)

Figure 13 compares the drag coefficients from the Gold Rider Leyland Cypress and Bakers Blue Spruce with their tube bank equivalents. While the match is not expected to be

perfect given the difference in skin friction, shape, and so on, the drag coefficient of each

configuration is comparable.

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Fig. 11. Tube bank experimental setup with schematic drawing

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0 1 2 3 4 5 6 7 8 9 10

0

0.05

0.1

0.15

0.2

0.25

0.3

Resistance Coefficient

Experiment

Idelchik's Emprical Model

Fig. 12. Comparison between measured and calculated resistance coefficients of tube banks

Table 3. Parameters used in comparing vegetation with a comparable tube bank configuration

β (%) κ (m−1) D (mm) Pos.

Veg. Tubes Veg. Tubes Veg. Tubes Rows Tubes

Row L

0

(cm)

Blue Spruce

A 1.8 1.8 2.4 2.4 9.4 10.6 5 10 10.0

B 1.8 1.8 2.6 2.6 8.6 9.5 7 9 7.1

C 1.8 1.7 2.3 2.3 9.7 11.2 4 11 12.5

D 1.8 1.8 2.5 2.5 8.9 10.4 4 13 12.5

Cypress

A 1.4 1.4 2.1 2.2 8.3 8.9 7 8 7.1

B 1.4 1.4 1.9 2.0 9.2 10.7 3 13 16.7

C 1.4 1.4 2.2 2.2 8.1 9.3 4 13 12.5

D 1.4 1.4 1.9 1.9 9.4 10.2 6 7 8.3

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Fig. 13. Drag coefficient comparison between vegetation sample configurations [Bakers Blue

Spruce (β=1.8%) and Gold Rider Leyland Cypress (β=1.4%)] and their corresponding tube bank

configuration with respect to velocity. Tube bank configurations were determined using Eq. 10 and

by approximating the geometric parameters (β, κ, and D) of the vegetation shown in Table 3. The

tube bank geometric parameters are also shown in Table 3.

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6. Conclusion

This report documents a series of experiments implemented to determine the absorption

coefficient, pressure loss, and the solid fraction of different types of vegetation sample configurations. The primary objective of this work was to calculate the drag coefficients of bulk

vegetation that can be incorporated into CFD models. In addition to establishing drag coefficients of bulk vegetation, notable findings regarding vegetation structure and similarities

between drag coefficients of plant species were also discovered from this work. It cannot

be concluded, however, that the findings from this work applies to all bulk vegetation, but

exclusively to the samples studied in these experiments.

To summarize, the findings of this work are as follows:

1. The calculated absorption coefficient for each sample demonstrated a strong relationship with its corresponding solid fraction.

2. The overall average drag coefficient of the bulk vegetation was found to be 2.8 with

an expanded uncertainty of 0.4. The differences between the average drag coefficients of different plant species as well as the leaf type groups were shown to be

significant, while still falling within the overall mean’s uncertainty bound, suggesting that the overall average drag coefficient could be used as a constant value in CFD

models of various plant types.

3. Compared to previous works, the overall drag coefficient reported in this work is

higher than any value reported in past studies [2–6] by a factor of 2 or more. It

should be noted that this difference could significantly alter the burning rate behavior of vegetation in CFD calculations. The experimental method of this work was

verified using tube banks with well-known drag laws. The experimental setup from

this study reproduced these drag coefficients. The difference in drag coefficient from

previous work is likely related to fact that in our experimental setup the flow is forced

through the vegetation, instead of having a path around the vegetation. Our setup is

intentionally designed to mimic computational cells in a CFD calculation, in which

the vegetation is treated as a collection of subgrid Lagrangian particles.

Acknowledgments

The authors would like to thank Matthew Bundy and Artur Chernovksy of the National

Fire Research Laboratory at NIST, who assisted in conducting these experiments and in

processing the data.

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References

[1] K. McGrattan, S. Hostikka, R. McDermott, J. Floyd, C. Weinschenk, and K. Overholt.

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of Finland, Espoo, Finland, sixth edition, September 2013. Vol. 1: Mathematical

Model; Vol. 2: Verification Guide; Vol. 3: Validation Guide; Vol. 4: Software Quality

Assurance. 1

[2] J. Cao, Y. Tamura, and A. Yoshida. Wind tunnel study on aerodynamic characteristics

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[3] J. Jalonen and J. Jarvel  ̈ a. Estimation of drag forces caused by natural woody vegeta-  ̈

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[4] G.J. Mayhead. Some Drag Coefficients for British Forest Trees Derived from Wind

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[5] J. A. Gillies. Drag coefficient and plant form response to wind speed in three

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107(D24):ACL 10–1–ACL 10–15, 2002.

[6] H. Ishikawa, A. Suguru Amano, and Y. Kenta. Flow around a Living Tree. JSME

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2006. 1, 17, 21

[7] F. Pimont, J.L. Dupuy, R. R. Linn, and S. Dupont. Validation of FIRETEC wind-flows

over a canopy and a fuel-break. Int. J. Wildland Fire, 18(7):775–790, Oct. 2009. 1

[8] S. Dupont and Y. Brunet. Edge flow and canopy structure: a large-eddy simulation

study. Boundary Layer Meteorology, 126(1):51–71, Jan. 2008. 1

[9] E. Mueller, W. Mell, and A. Simeoni. Large eddy simulation of forest canopy flow

for wildland fire modeling. Canadian J. Forest Res., 44(12):1534–1544, Jul. 2014. 2

[10] Emerson Process Management Rosemount Measurement, Chanhassen, Minnesota,

USA. Rosemount Annubar® Primary Flow Element Flow Test Data Book, July 2009.

6, 25

[11] D Lane and N Salkin. Tukey’s honestly significant difference (hsd). N. Salkind der.),

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[12] B. Toman and A. Possolo. Laboratory effects models for interlaboratory comparisons.

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[13] A. Gelman, J. Carlin, H. Stern, and D. Rubin. Bayesian Data Analysis, 2nd Edition.

Chapman and Hall/CRC, 2013. 15

[14] David Lunn, David Spiegelhalter, Andrew Thomas, and Nicky Best. The bugs project:

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[15] I.E. Idelchik. Handbook of Hydraulic Resistance, 3rd Edition. CRC Press, Inc., 1994.

17

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A. Uncertainty Analysis of the Drag Coefficient

The drag coefficient was calculated using a combination of Eqs. (6) and (7):

Cd =

−2∆P

ρU2ln W

(A.1)

where ∆P is the pressure drop across the vegetation sample, measured with a pressure

transducer, ρ is the air density, obtained via pressure, temperature, and relative humidity

measurements and the ideal gas law, U is the average velocity of air through the wind

tunnel, measured using an Annubar, and W is the free area coefficient of the vegetation,

measured using photography and image analysis. The uncertainty of the measured drag

coefficient was estimated using the law of propagation of uncertainty after determining the

drag coefficient:

uc =

s

∂Cd

∂∆P

u∆P

2

+



∂Cd

∂ ρ uρ

2

+



∂Cd

∂U

uU

2

+



∂Cd

∂W

uW

2

(A.2)

A coverage factor of 2 is applied to the combined uncertainty to produce a 95 % confidence

interval.

A.1 Pressure

Two pressure transducers were used in this study. Transducer 1 measured the differential

pressure across the vegetation while Transducer 2 measured the differential pressure across

the Annubar. The Type A evaluation of standard uncertainty of the pressure difference, ∆P,

was taken as the standard deviation, s∆P, of the measurements sampled at 90 Hz for 30 s.

The Type B evaluation of standard uncertainty was determined from the calibration error

sources of the pressure transducers and was found to be ucal = 1.4 Pa and ucal = 1.5 Pa for

Transducers 1 and 2, respectively. The combined uncertainty was found via quadrature:

u∆P =

q

u

2

cal +s

2

∆P

(A.3)

A.2 Air Density

The density of air was determined from the absolute pressure, temperature, and relative

humidity readings obtained simultaneously with the wind tunnel measurements:

ρ =

P

RT

(A.4)

where T is the measured air temperature, P is the absolute pressure , and R is the specific

gas constants for air (287 J/(kg ·K). The Type A evaluation of uncertainty of air density was

determined from the standard uncertainty of the absolute pressure, sP, and temperature, sT ,

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readings of the testing facility. The Type B evaluation of air density was determined from

the error sources in the instrauments, uinst., used to measure the absolute pressure (1 %

accuracy of the pressure gauge) and temperature (1.5 ◦C) of air in the testing facility. The

combined uncertainty of the pressure and temperature was found via quadrature:

uP =

q

u

2

inst. +s

2

P

(A.5)

uT =

q

u

2

inst. +s

2

T

(A.6)

The standard uncertainty of the air density was determined through the law propagation of

uncertainties:

uρ =

s

∂ ρ

∂P

uP

2

+



∂ ρ

∂T

uT

2

(A.7)

A.3 Velocity

The average air velocity through the wind tunnel, U, was measured using an Annubar and

calculated using the following formula:

U = K

s

2∆P

ρ

(A.8)

where K is a flow coefficient and ∆P is the pressure difference measured by Transducer 2

discussed above. The Type B evaluation of standard uncertainty of the flow coefficient was

assumed to be 5 % of the reading6. The standard uncertainty of the velocity was determined

through the law of propagation of uncertainties:

uU =

s

∂U

∂∆P

u∆P

2

+



∂U

∂ ρ uρ

2

+



∂U

∂K

uK

2

(A.9)

A.4 Free-Area Coefficient

The uncertainty of the free-area coefficient was determined by measuring the projected

areas of objects with known dimensions using the same photographic method described in

Section 3.2. The standard deviation of the difference between the measured and true freearea coefficients was found to be uW = 0.01, which was treated as a Type B evaluation of

standard uncertainty for all free-area coefficients of the vegetation samples.

6A 485 Calibrated Annubar is reported to have an accuracy of 0.5 % in circular ducts as reported by [10].

However, since an Annubar was used in a square duct in these experiments, the uncertainty of the flow

coefficient was adjusted to 5 % after contacting the manufacturer.

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B. Uncertainty Analysis of the Absorption Coefficient

The absorption coefficient was calculated by adjusting Eq. (6)

κ =

−ln W

L

(B.1)

where W is the relative fraction of light passing through a distance of L, also known as

the free-area coefficient. The uncertainty of the free-area coefficient, W, is discussed in

Appendix A.4. Vegetation samples trimmed using the guiding frame were found to have

a standard deviation of for their respective cubic lengths of 5.0 mm which was treated as

a Type B evaluation of standard uncertainty. The standard uncertainty of the absorption

coefficient was determined through the law of propagation of uncertainties:

uκ =

s

∂ κ

∂W

uW

2

+



∂ κ

∂L

uL

2

(B.2)

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C. Uncertainty Analysis of the Solid Fraction of Vegetation

The solid fraction of vegetation was calculated using the following formula

β =

Vveg. −Vabs.water

Vtotal

(C.1)

where Vveg., Vabs.water, and Vtotal are the volumes of the vegetation, absorbed water, and total

occupancy (0.125 m3), respectively. The standard uncertainty of the solid fraction was

determined through the law of propagation of uncertainties:

uβ =

s

∂ β

∂Vveg.

uVveg.

2

+



∂ β

∂Vabs.water

uVabs.water2+



∂ β

∂Vtotal

uVtotal2(C.2)

C.1 Volume of Vegetation

The combined standard uncertainty of the measured solid sample volume combines, via

quadrature, the Type A standard uncertainty, taken as the standard deviation of the repeated

measurements, and the Type B standard uncertainty, taken as the standard deviation of

the assumed uniform distribution that characterizes the uncertainty in the reading of the

graduated cylinder, 5/

√

12 mL, where the cylinder has 5 mL grading divisions.

C.2 Volume of Water Absorbed

The volume of water absorbed in the vegetation was determined from the difference in

mass of the vegetation before and after water discplacement tests divided by the density of

water at room temperature (1.0 g/mL). The mass of the vegetation was measured using a

Mettler Toledo load cell. The uncertainty of the measured mass was assumed to be 5 g and

was treated as a Type B standard uncertainty for all mass measurments.

C.3 Volume of Total Occupancy

The uncertainty of the volume of total occupancy was determined from the uncertianty of

the cubic length described in Appendix B.

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