lin_2006_journal-of-wind-engineering-and-industrial-aerodynamics.pdf

ARTICLE IN PRESS

Journal of Wind Engineering

and Industrial Aerodynamics 94 (2006) 51–76

0167-6105/$ -

doi:10.1016/j

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Investigation of plate-type windborne debris.Part I. Experiments in wind tunnel and full scale$

Ning Lina, Chris Letchforda,�, John Holmesb

aCivil Engineering, Texas Tech University, P.O. Box 41023, Lubbock, TX 79409, USAbJDH Consulting, P.O. Box 269, Mentone, Victoria 3194, Australia

Received 30 December 2004; received in revised form 26 September 2005; accepted 6 December 2005

Available online 10 January 2006

Abstract

Modeling of the trajectory of windborne debris for incorporation in wind hazard risk assessment

requires the knowledge of debris aerodynamics. On-going experiments to determine the flight

characteristics of various types of debris are being carried out in the Texas Tech University (TTU)

wind tunnel. This paper investigates the aerodynamic characteristics of plate-type debris. Useful data

are presented in dimensionless form. Empirical expressions for estimating the horizontal flight speed

and distance are derived. Results from wind-tunnel experiments are in reasonable agreement with

those from full-scale tests. These results can be used to validate numerical calculations of trajectories

of plate-type windborne debris.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Debris; Plate type; Hurricane; Trajectory; Aerodynamics; Wind tunnel

1. Introduction

Debris is a major cause of damage and building destruction in strong wind events suchas hurricanes and tornadoes. Potential debris includes roof gravel, roof members, andother building components, as well as tree limbs and vehicles. In hurricanes, strongsustained winds that only change direction slowly often lead to building failures thatlaunch debris into the wind field, causing a cascade of subsequent building damage. In a

see front matter r 2005 Elsevier Ltd. All rights reserved.

.jweia.2005.12.005

ote that Part II: Investigations of plate-type windborne debris – Part II: Computed Trajectories, has

ed in Journal of Wind Engineering & Industrial Aerodynamics, Volume 94, issue 1, (2006) pp. 21–39.

nding author. Tel.: 1 806 742 3476; fax: 1 806 742 3446.

dress: [email protected] (C. Letchford).

www.elsevier.com/locate/jweia

ARTICLE IN PRESSN. Lin et al. / J. Wind Eng. Ind. Aerodyn. 94 (2006) 51–7652

tornado, the faster speeds combined with a vertical component tend to pick up heavierdebris items and sustain them in the wind field, allowing them to accelerate to much highervelocities. This fast-flying debris may cause loss of human life and great damage tobuilding surfaces. Once the envelopes of buildings are penetrated, internal pressurizationapproximately double the loads on suction zones, a phenomenon often sufficient to causefailure of roofing and wall cladding which generates new debris.The problem of debris may be summarized as one of flight initiation, flight trajectory

(involving travel time, distance, and velocity), and impact. Wills et al. [1] classified debrisinto three generic types: compact, plate-like, and rod-like, and studied the flight initiationfor each. Wang and Letchford [2] studied the flight initiation of plate-like objects in a windtunnel; the test results compared favorably with the model of Wills et al. Wills et al. [1] alsoestablished a damage model of debris impact as a function of debris velocity. However,debris velocity itself has received little attention. This is despite there being a number ofstandard impact test specifications (e.g., [3,4]) which have largely been developed frompost-damage investigations, with little research on the aerodynamics of flying debris.Knowledge of debris aerodynamics and proper estimation of debris trajectory arenecessary to establish rational impact criteria and risk assessment models.Research on flight behavior and trajectory of debris has been undertaken sporadically

since the 1970s, e.g., Lee [5,6] and Twisdale et al. [7] studied missile transport in tornados.Assumptions about debris aerodynamics were made to calculate debris trajectories. In the1980s, Tachikawa [8,9] first conducted experiments on flat plates in a wind tunnel, andrevealed the existence of flight modes occurring as a function of the initial angle of attack.Tachikawa [8] established non-dimensional equations of debris motion and introduced anon-dimensional parameter K describing the flight behavior based on both flow and debrischaracteristics. Holmes et al. [10] describe numerical modeling of cube and platetrajectories. Baker [11] also made an analytical and numerical study of debris flightbehavior, using an alternative non-dimensional form.Model experiments to determine the flight characteristics of the three generic types of

debris have been carried out in the Texas Tech University (TTU) wind tunnel. Full-scaletests on plates were also conducted, using a C-130 aircraft to generate strong winds. Thispaper presents these experimental studies of plate-type debris. The experimentalprocedures are described in detail. Flight features of plates are examined, including themode of motion, trajectory, and velocities, all of which are affected by the wind field,model characteristics, and initial support configuration. Data are interpreted inTachikawa’s non-dimensional form [8]. Simple empirical expressions are derived toestimate the horizontal flight speed (with given flight distance) and flight distance (at givenflight time) of plate-type debris. Wind-tunnel and full-scale test results are in reasonableagreement. These expressions may be used to establish rational debris impact test criteria.Part 2 of this paper [12] presents numerical modeling of the flight of plate-type objects, andcompares computed trajectories with the experimental results.

2. Experiments

2.1. Wind-tunnel experiments

Model experiments were carried out in the closed circuit 1.8m wide by 1.2m high windtunnel at TTU. The wind tunnel was cleared of all roughness elements. The turbulence

ARTICLE IN PRESSN. Lin et al. / J. Wind Eng. Ind. Aerodyn. 94 (2006) 51–76 53

intensity varied from 0.5% at launch position in the center of the wind tunnel to about 3%in the wall boundary layers approximately 250mm thick. A circular electromagneticsupport (diameter b ¼ 18mm) was placed 0.6m high and 6.65m in front of a catch net. ABK Precision DC power supply provided a steady 12V potential to the electromagnet.Small metal tabs glued to the models held them to the magnet. A schematic drawing of the

debris model, ρm,

electromagnet

h

D

b

Wind, U, ρa

B- perpendicular to flow

X

Z

um

vm

Um

debris velocities

�0

Fig. 1. Diagram of debris launch support in wind tunnel.

Table 1

Plate models for the wind-tunnel experiments

Plate no. Material Size (B�D� h) (mm�mm�mm) Mass (g) D=B h=ffiffiffiffiffiffiffi

BDp

ð%Þ b/B (%)

#1 Basswood 26� 26� 9 3.8 1.00 34.6 69.2

#2 Balsa 40� 40� 1.5 1.1 1.00 3.75 45.0

#3 Plastic 42� 42� 2 5.1 1.00 4.76 42.9

#4 Balsa 50� 50� 3 2.1 1.00 6.00 36.0

#5 Plywood 50� 50� 6 11.1 1.00 12.0 36.0

#6 Balsa 55� 55� 3 2.6 1.00 5.45 32.7

#7 Balsa 75� 75� 3 3.2 1.00 4.00 24.0

#8 Plywood 75� 75� 3 12.3 1.00 4.00 24.0

#9 Plywood 75� 75� 6 22.3 1.00 8.00 24.0

#10 Basswood 75� 75� 9 24.8 1.00 12.0 24.0

#11 Basswood 76� 76� 1.5 5.0 1.00 1.97 23.7

#12 Aluminum 76� 76� 1.5 25.2 1.00 1.97 23.7

#13 Floppy disc 90� 90� 2.5 15.0 1.00 2.78 20.0

#14 Basswood 150� 50� 9 31.7 0.30 10.4 12.0

#15 Plastic 120� 50� 1 10.5 0.42 1.29 15.0

#16 Balsa 126� 56� 4.5 4.0 0.44 5.36 14.3

#17 Basswood 126� 56� 4.5 5.7 0.44 5.36 14.3

#18 Plywood 120� 75� 3 19.0 0.63 3.16 15.0

#19 Plywood 75� 120� 3 19.0 1.60 3.16 24.0

#20 Balsa 56� 126� 4.5 4.0 2.25 5.36 32.1

#21 Plastic 50� 120� 1 10.5 2.40 1.29 36.0

#22 Basswood 50� 150� 9 31.7 3.00 10.4 36.0

ARTICLE IN PRESS

Table 2

Plate debris for the full-scale tests

Plate no. Material Size (B�D� h) (m�m�m) Mass (kg) D/B h=ffiffiffiffiffiffiffi

BDp

ð%Þ

C2 3/800 MDF 2.46� 1.24� 0.0095 22.5 0.50 5.44

D1 Tempered Hardboard+Styrofoam

2.44� 1.22� 0.025 15.0 0.50 14.5

D2 2.44� 1.22� 0.025 19.3 0.50 14.5

E1 3/400MDF 2.46� 1.24� 0.019 43.2 0.50 10.9

E2 2.46� 1.24� 0.019 42.5 0.50 10.9

E3 2.46� 1.24� 0.019 43.7 0.50 10.9

E4 1.24� 2.46� 0.019 46.2 2.00 10.9

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t (m

)


(a)

(b)

(c)

Fig. 2. Analysis of debris trajectory. (a) Trajectories of plate #8, U ¼ 9.1 m/s (a0 ¼ 01), (b) trajectories of plate #8,

U ¼ 21:5m=s (a0 ¼ 01), (c) trajectories of plate #8, U ¼ 16:4m=s (a0 ¼ 01).

N. Lin et al. / J. Wind Eng. Ind. Aerodyn. 94 (2006) 51–7654


debris launch support is shown in Fig. 1. In this figure and throughout the study, debrisflight coordinates are x—horizontal displacement, z—vertical displacement, S—resultantdisplacement, and t—flight time; debris velocity components are um—horizontal debrisvelocity, vm—vertical debris velocity, and Um—resultant debris velocity; dimensions of adebris model are h—thickness, B—width perpendicular to flow, D—length parallel to flow;rm—debris density; ra—air density; U—wind speed; a0—initial angle of attack.

Wind velocities were measured by a 4-hole Cobra Probe (T.F.I. Series 100) locatedadjacent to the launch support. Switching off the current to the electromagnet allowed thedebris to begin flight at any desired wind speed. An Olympus American Encore MAC PCIversion 2.18 digital video camera (60Hz, 0.0167 second per frame) was used to captureflight paths. Flight time and coordinates were obtained from the images. Parallaxcorrections were made to flight paths assuming that the object stayed largely on thecenterline plane of the wind tunnel. Flight speeds were calculated from the corrected dataof flight time and coordinates.

0

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pla

te s

pee

d /

win

dsp

eed

Um

Um (d s/ dt )

um

um (d x/ dt )

0

pla

te s

pee

d /

win

d s

pee

d

Um = ∆s / ∆t

Um = ds / dt

um = ∆s / ∆t

um = ds / dt

Um = ∆s / ∆t

Um = ds / dt

um = ∆s / ∆t

um = ds / dt

(a)

(b)

Fig. 3. Calculation of debris horizontal and resultant velocities. (a) Plate #8, U ¼ 9.1m/s, a0 ¼ 01, (b) Plate #8,

U ¼ 16:4m=s, a0 ¼ 01.


Twenty-two plate models were used. The plate materials included wood, plastic, andaluminum, so as to provide a wide variety of densities. The square and rectangular platesranged in weight from 1.1 to 31.7 g and in side length from 26 to 150mm. Wind speedsranged from 4.5 up to 26m/s. Model dimensions and wind speeds were designed to providea range of debris side ratio, support condition, and the Tachikawa parameter K (2.2–32 inthis study). The details of the plate models are shown in Table 1.All models were released at an initial angle of attack, a0 of 01. In order to investigate the

effects of initial angle of attack on debris trajectory, a square plate (#8), two rectangularplates (#15 and #21) were also tested at other initial angles of attack. All models weresupported at the center. A square plate (#3) supported at different places was also tested toinvestigate the influence of initial support. Three trials were undertaken for each case.

2.2. Full-scale tests

Full-scale tests were conducted with a C-130 Hercules aircraft to simulate strong winds,at the west runway of Reese Technology Center, Lubbock, Texas. The site is characterizedas Exposure Category C in ASCE 7. Previous experiments demonstrated that the propellerwash of a C-130 aircraft is suitable for use as a source of extreme winds [13]. Table 2 showsdetails of the full-scale debris which mainly consisted of rectangular 4 ft� 8 ft plate debrisranging in weight from 15 to 45 kg. The plates were launched from a 1m high table in thefield. Wind velocities were measured by an RM Young propeller/vane anemometer located1m high and 1m upstream of the launch table. The same camera used in the wind-tunneltests was employed here.

3. Data analysis

In the wind tunnel, each of the plate models was tested at increasing wind speeds untilthe plate hit the wind-tunnel ceiling. The coordinates and the time intervals were exported

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Ver

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cem

ent

(m)

U=8.5 m/s

10 m/s

10.8 m/s

11.9 m/s

13.9 m/s

15.3 m/s

16.3 m/s

18.0 m/s

20.8 m/s

1 3 5

Fig. 4. Plate trajectories at different wind speeds (Plate #8, ra=rm ¼ 0:0015, D=B ¼ 1, h=ffiffiffiffiffiffiffi

BDp

¼ 4%,

b=B ¼ 24%, a0 ¼ 01, s center).


from the digital camera file to EXCEL spreadsheets. The data were analyzed to determinehorizontal displacements, vertical displacements, and velocities. Parallax corrections wereundertaken at this stage. Time nominally started at the moment of release.

Fig. 2 shows examples of trajectory analyses for one plate model (#8) at three differentspeeds. As shown in Fig. 2a, at a relatively low wind speed, each trial of a plate had quiteconsistent trajectories when falling. This consistency was also apparent at high wind speedswhen the plate flew up (Fig. 2b). Fig. 2c shows that, at a critical wind speed, trialspresented some differences. However, these differences are predominately in the vertical

Horizontal displacement (m)

Ver

tica

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pla

cem

ent

(m)

# 7

# 8

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0

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0 2 4 61 3 5

Fig. 5. Plate trajectories affected by debris density (U ¼ 12:5m=s, D=B ¼ 1, h=ffiffiffiffiffiffiffi

BDp

¼ 4%, b=B ¼ 24%, a0 ¼ 01,

s center).

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pla

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(m)

#13 2.78 %

# 8 4.0 %

# 9 8.0 %

h / √BD

531

Fig. 6. Plate trajectories affected by geometrical feature h=ffiffiffiffiffiffiffi

BDp

(U ¼ 18.1m/s, ra=rm ¼ 0:0015, D=B ¼ 1,

b=B ¼ 20224%, a0 ¼ 01, s center).


direction. Horizontal displacements are practically constant for each trial of a plate at agiven wind speed.Fig. 3 shows examples of velocity analyses for one model (#8) at two different

wind speeds. Both horizontal (um) and resultant (Um) velocities were calculated bytwo methods. The first method used discrete displacements to calculate velocities:um ¼ Dx=Dt (Um ¼ DS=Dt), with Dt � 0:083 s (five video frames). The second methodinvolved fitting best fit polynomials to the displacements and differentiating to obtainvelocities: um ¼ dx=dt (Um ¼ dS=dt), in which xðtÞ and SðtÞ are fitted polynomialfunctions (R2 values over 0.99). The second method results in smooth graphs. Although theresults from the second method do not reflect the real debris velocity very well at thebeginning of flight, the two methods yield close results for the portions of high-debris flightspeed. At a relatively low wind speed, the resultant velocity of a plate is higher thanits horizontal velocity due to the relative importance of its vertical velocity component(Fig. 3a), while at a higher wind speed, the resultant and horizontal velocities aremuch closer (Fig. 3b). This difference in velocities reflects the influence of the lift force onthe debris. The closer the two curves, the smaller is the vertical velocity (vm), whichindicates the greater the lift force sustaining the debris flight and counteracting the effectsof gravity.Horizontal and resultant plate velocities used in the following discussion were obtained

by averaging the results from the two calculation methods. The vertical velocity wascalculated using the first method (vm ¼ Dz=Dt).Non-dimensional analyses were undertaken with non-dimensional variables

according to Tachikawa’s non-dimensional equations of debris motion [8]: horizontaldisplacement (x ¼ gx=U2), horizontal velocity (u ¼ um=U), vertical displacement(z ¼ gz=U2), vertical velocity (v ¼ vm=U), resultant velocity (Um ¼ Um=U), and time(t ¼ gt=U).

#7 K=9.1

#8 K=4.6

#9 K=3.0

#10 K=2.2

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Fig. 7. Plate trajectories affected by K ¼ raU2=2hgrm. (D=B ¼ 1, b=B ¼ 24%, a0 ¼ 01, s center).


4. Results and discussion

4.1. Flight behavior of plates in the wind tunnel

The experimental results indicate that, for a certain debris shape, the debris trajectory(T) is a function of at least nine parameters: wind speed (U), air density (ra), platedimensions (B, D, and h), plate density (rm), support dimension (b), support position(s, e.g., center, corner, or edge), and initial angle of attack (a0), and can be expressed as

T ¼ f ðU ; ra; rm; h; B; D; b; s; a0Þ. (1)

The variations of two-dimensional plate trajectories within these parameters wereinvestigated. Fig. 4 shows the trajectories of plate #8 at wind speeds ranging from 8.5 to20.8m/s. The higher the wind speed, the higher the flight path. Fig. 5 shows the effect of

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#6 D/B=1

#20 D/B=2.25

#15 D/B=0.42

#18 D/B=0.63

#13 D/B=1

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0

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(a)

(b)

Fig. 8. Plate trajectories affected by geometrical feature D/B. (a) D=BX1 (K ¼ 6:7, b=B ¼ 33%, a0 ¼ 01, s

center), (b) D=Bp1 (K ¼ 6:7, b=B ¼ 15220%, a0 ¼ 01, s center).


plate density on plate trajectories. With the same geometric dimensions but lower density,plate #7 (ra=rm ¼ 0:0057) flew higher than plate #8 (ra=rm ¼ 0:0015), at the same windspeed. Fig. 6 shows the effect of plate dimension h on plate trajectories. Comparison oftrajectories of three square plates (h=

ffiffiffiffiffiffiffi

BDp

¼ 2:8� 8:0%) with similar b/B (20–24%)clearly show that the lift force increases with decreasing h=

ffiffiffiffiffiffiffi

BDp

, and overcomes gravity toaccelerate the plate into the air.The effects of U, ra, rm, and h on debris trajectories can be presented using the non-

dimensional Tachikawa parameter K ¼ raU2A=2mg ¼ raU

2=2ghrm [8], the ratio of

#10 b/B=24%

#1 b/B=69%

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Fig. 9. Plate trajectories affected by relative support dimension b/B (K ¼ 7.6, D/B ¼ 1, a0 ¼ 01, s center).

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(m) #3 center

#3 corner#3 edge

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Fig. 10. Plate trajectories affected by support place s (K ¼ 3.37, D/B ¼ 1, b/B ¼ 43%, a0 ¼ 01).

ARTICLE IN PRESS

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0 1 2 3 4

(a) (b)

(c) (d)

(e) (f)

Fig. 11. Variations in mode of motion and trajectory with initial angle of attack a0 (deg). (a) Plate #8 (D/B ¼ 1, b/

B ¼ 24%, s center), K ¼ 5.9, (b) Plate #8, K ¼ 11, (c) Plate #15 (D/B ¼ 0.42, b/B ¼ 15%, s center), K ¼ 4.5, (d)

Plate #15, K ¼ 12.5, (e) Plate #21 (D/B ¼ 2.4, b/B ¼ 36%, s center), K ¼ 4.5, (f) Plate #21, K ¼ 11.2.

N. Lin et al. / J. Wind Eng. Ind. Aerodyn. 94 (2006) 51–76 61


aerodynamic force to gravity force. Reducing the parameters, Eq. (1) can be rewritten as

T ¼ f ðK ; D=B; b=B; a0; sÞ. (2)

Fig. 7 shows the trajectories of four square plates with different values of K whileholding the values of the other parameters constant. As expected, plate trajectories rise asK increases.The side ratio (D/B), another plate geometrical feature, also affects the trajectory. As

shown in Fig. 8, given the same K value and holding the other dimensionless parametersconstant, the smaller the side ratio, the higher the plate flies. The trajectory variation isgreater when D=B41 than when D=Bo1.In addition to K and D/B, three initial support configuration factors significantly

affected the plate trajectories: b, s, and a0. Fig. 9 presents the influence of the supportdimension. Given the same K, the trajectories of plate #10 (b/B ¼ 24%) and plate #1(b=B ¼ 69%) show that the smaller the ratio of support diameter to plate width (b/B), the

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#7 K=9.1

#8 K=4.6

#9 K=3.0

#10 K=2.2

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#7 K=9.1

#8 K=4.6

#9 K=3.0

#10 K=2.2

51 2 3

1

Fig. 12. Horizontal plate trajectories affected by K ¼ raU2=2hgrm (D/B ¼ 1, b/B ¼ 24%, a0 ¼ 01, s center).


larger the initial lift force, increasing the flight altitude. Fig. 10 shows the trajectories ofplate #3 supported at the center, corner, and edge, respectively, at a given wind speed.When the support was at the center of the plate, the lift force developed on the front half ofthe plate was largely unaffected by the support; however, when the support was at themiddle of the plate’s leading edge, gross disturbance to the flow occurred at the critical liftgeneration position, lowering the altitude of the plate’s flight. Support at a corner of theplate resulted in a combination of these two effects.

Video records show that the trajectory pattern of a plate depends mainly on its mode ofmotion, which in turn is closely related to the initial angle of attack (a0). Fig. 11 shows, atdifferent a0, the trajectories of square plate #8 (a,b), rectangular plate #15 (D=B ¼ 0:42)(c,d), and rectangular plate #21 (D=B ¼ 2:4) (e,f) at relatively low and high values of K.Tachikawa [8] defined three flight modes for plates: auto-rotating, intermediate, andtranslatory. In these tests, generally at a0 ¼ 0 and a0 ¼ 15�, plates entered into clockwiseauto-rotation and ‘flew up’ over long distances. At a0 ¼ 45� and a0 ¼ 90�, the intermediatemode changed from clockwise to counter-clockwise rotation at initial stages of flight andthen to translatory mode at 451 to horizontal before hitting the ground. For a0 ¼ 135�, atrelatively low wind speeds, one or two counter-clockwise rotations were followed bytranslatory mode, also at 451 to ground. However, as wind speed increases, the translatorymode of plates may change to clockwise rotation and the plates ‘fly up’ (b, d, and f). Ata0 ¼ 165�, plates entered into counter-clockwise auto-rotation. It was noted that at

00 1 2 3 4 5 6

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0 1 2 3 4 5 6Horizontal displacement (m)

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#20 D/B=2.25

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5

6

0 0.2 0.4 0.6 0.8 1.2Time (sec)

Ho

rizo

nta

l dis

pla

cem

ent

(m)

#6 D/B=1

#20 D/B=2.25

#15 D/B=0.42

#18 D/B=0.63

#13 D/B=1

0

1

2

3

4

5

6

#15 D/B=0.42

#18 D/B=0.63

#13 D/B=1

1

0 0.2 0.4 0.6 0.8 1.2Time (sec)

Ho

rizo

nta

l dis

pla

cem

ent

(m)

1

(a)

(b)

Fig. 13. Horizontal plate trajectories affected by side ratio (D/B). (a) D=BX1 (K ¼ 6.7, b/B ¼ 33%, a0 ¼ 01, s

center), (b) D=Bp1 (K ¼ 6.7, b/B ¼ 15–20%, a0 ¼ 01, s center).


a0 ¼ 15�, plate #15 (D/B ¼ 0.42) had relatively low flight paths at both low and high windspeeds (c,d), and that at a0 ¼ 165�, its initial counter-clockwise rotation changed toclockwise at high wind speed and the plate flew up (d).

4.2. Horizontal trajectories of plates in the wind tunnel

Although plate trajectories showed great variations in the vertical direction with each ofthe five parameters in Eq. (2), the horizontal component of the plate trajectories showed

0

0.2

0.4

0.6

0.8

1

1.2


Ho

rizo

nta

l sp

eed

/ W

ind

sp

eed

#10 b/B=24%

#1 b/B=69%

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1 1.2Time (sec)

Ho

rizo

nta

l dis

pla

cem

ent

(m) #10 b/B=24%

#1 b/B=69%

531

Fig. 14. Horizontal plate trajectories affected by b/B (K ¼ 7.6, D/B ¼ 1, a0 ¼ 01, s center).


certain patterns. Figs. 12–16 show the effect of each of the parameters on horizontal platetrajectories, in terms of horizontal velocity versus horizontal displacement, and horizontaldisplacement versus flight time.

It was seen in Fig. 7 that plate trajectories rise as K increases. K also greatly affects thehorizontal component of plate trajectories. Fig. 12 shows that horizontal speed (with agiven horizontal displacement) increases with K, as does the horizontal displacement (at agiven time).

Plate trajectories rise as side ratio (D/B) decreases (Fig. 8); however, D/B appears to onlyslightly affect plate horizontal trajectory. In Fig. 13(a), horizontal velocities (with a givenhorizontal distance) of plate #6 (D/B ¼ 1) and plate #20 (D/B ¼ 2.25) are quite close. Thehorizontal displacement (at a given time) of plate #20 is slightly less than that of plate #6.When D=B1, D/B has little influence on either velocity or horizontal displacement, as

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6Horizontal displacement (m)

Ho

rizo

nta

l sp

eed

/ W

ind

sp

eed

#3 center#3 corner#3 edge

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1.2Time (sec)

Ho

rizo

nta

l dis

pla

cem

ent

(m)

#3 center#3 corner#3 edge

1

Fig. 15. Horizontal plate trajectories affected by s (K ¼ 3.37, D/B ¼ 1, b=B ¼ 43%, a0 ¼ 00).

ARTICLE IN PRESS

0

0.2

0.4

0.6

0.8

1

0 4Horizontal displacement (m)

Ho

rizo

nta

l sp

eed

/ W

ind

sp

eed

0

0.2

0.4

0.6

0.8

1

Ho

rizo

nta

l sp

eed

/ W

ind

sp

eed

0 deg

15 deg45 deg

90 deg

135 deg

165 deg

0 deg

15 deg45 deg

90 deg

135 deg

165 deg

0 deg

15 deg45 deg

90 deg

135 deg

165 deg

0 deg

15 deg45 deg

90 deg

135 deg

165 deg

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)H

ori

zon

tal d

isp

lace

men

t (m

)

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Ho

rizo

nta

l dis

pla

cem

ent

(m)

0

1

2

3

4

5

6

2

2

6

0 4


6

(a)

(b)

Fig. 16. Horizontal trajectories affected by initial angle of attack a0 (deg) (Plate #8, D/B ¼ 1, b/B ¼ 24%, s

center). (a) K ¼ 5.9, (b) K ¼ 11.


shown in Fig. 13(b). This indicates that given the same value of K, square and rectangularplates present similar flight trajectories in the horizontal direction, even though they havedifferent aerodynamic coefficients.The effects of initial support configuration on the horizontal plate trajectories are also

very small. Fig. 14 shows that there is little influence of the support dimension (b/B) onhorizontal plate trajectories with the same K. Fig. 15 shows that plate #3 supported at thecenter, corner, and edge, respectively, followed an almost identical horizontal trajectory.Although the mode of motion, which is closely related to a0, greatly affects the platetrajectories in the vertical direction (Fig. 11), the corresponding horizontal trajectories arealmost independent of a0 (Fig. 16). Therefore, initial situation greatly influences thevertical trajectory of plates, but not the horizontal trajectory.


The investigation of two-dimensional trajectory of plate-like debris was extended tocompact- and rod-like debris. Although the results are not given herein, the horizontaltrajectories showed comparable characteristics to those of plates and are mainly dependenton K.

4.3. Non-dimensional horizontal trajectories of plates in the wind tunnel

In this section, the experimental data are presented according to Tachikawa’s non-dimensional scheme [8]. Since the horizontal trajectory of a particular debris type is mainlydependent on K, non-dimensional horizontal debris velocity, u, at a given non-dimensional

0

0.2

0.4

0.6

0.8

1

1.2

0.0 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0

0

0.2

0.4

0.6

0.8

1

1.2

0.0 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0

#1 #2 #3#4 #5 #6#7 #8 #9#10 #11 #12#13 #14 #15#16 #17 #18#19 #20 #21#22

#2 #3 #4#5 #6 #7#8 #9 #10#11 #12 #13#15 #16 #17#18 #19 #20#21

K

K

Uu mu

=Uu m

u =

(a)

(b)

Fig. 17. Non-dimensional horizontal plate velocities versus Tachikawa K. (a) x ¼ xg=U2 ¼ 0:05, (b)

x ¼ xg=U2 ¼ 0:1.


horizontal displacement, x, is a function of K. Fig. 17 shows this relationship for plates atgiven non-dimensional horizontal displacements. The data collapsed well at both a smallhorizontal displacement (x ¼ 0:05) (Fig 17a) and a large horizontal displacement (x ¼ 0:1)(Fig 17b), though u for some rectangular plates (#19 and #21) show relatively low values atx ¼ 0:1.

0

0.2

0.4

0.6

0.8

1

1.2

0.0 0.2 0.4 0.6 0.8 1.0

#14 (0.33) #15 (D/B=0.42)#17 (0.44) #18 (0.63)D/B=1 #19(1.6)#21 (2.4) #22 (3.0)

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

#14 (0.33) #15 (D/B=0.42)#17 (0.44) #18 (0.63)D/B=1 #19(1.6)#21 (2.4) #22 (3.0)

U2gx

x =

U

gtt =

Uu mu

=

U2

gxx =

Fig. 18. Non-dimensional plate trajectories in the horizontal direction (K ¼ 6).


Alternatively, the data showed that non-dimensional horizontal trajectories of plateswith different side ratios, with different initial support configurations, and at a range ofwind speeds, collapsed for each K (2pKp32 in the experiments). Fig. 18 is an example ofhorizontal trajectories of plates when K equal to 6. The data show that non-dimensionaldebris horizontal velocity with given K is primarily a function of non-dimensionalhorizontal displacement, which is a function of non-dimensional flight time.

0

0.2

0.4

0.6

0.8

1

1.2

0.00 1.00 2.00 3.00 4.00 5.00

#1 #2 #3#4 #5 #6#7 #8 #9#10 #11 #12#13 #14 #15#16 #17 #18#19 #20 #21#22

u = 1 - e-√1.8Kx

u

K x

Fig. 19. Horizontal trajectory of plate-type debris (u versus Kx).

0

1

2

3

4

5

6

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

#1 #2 #3 #4#5 #6 #7 #8

#9 #10 #11 #12#13 #14 #15 #16#17 #18 #19 #20#21 #22

Eq.(6)

Kx

K t

Fig. 20. Horizontal trajectory of plate-type debris (Kx versus Kt).


u depends on both x and K, and x depends on both t and K. When combining K withthese non-dimensional variables, all experimental data for plates collapse well in Figs. 19and 20, as u versus Kx and Kx versus Kt, respectively. This combination is consistent withBaker’s non-dimensional equation of debris motion in the horizontal direction [11]. It isnoted that the gravitational constant, g, is cancelled in both Kx and Kt.The data in Fig. 19 show that for the observed debris trajectory, u can be approximated

by an exponential function of Kx

u ¼ 1� e�ffiffiffiffiffiffiffiffiffi

2CKxp

. (3)

0

0.2

0.4

0.6

0.8

1

1.2

0.00 1.00 2.00 3.00 4.00 5.00

#1 #2 #3

#4 #5 #6

#7 #8 #9

#10 #11 #12

#13 #14 #15

#16 #17 #18

#19 #20

#21 #22

u

Kx

0

0.2

0.4

0.6

0.8

1

1.2

0.00 1.00 2.00 3.00 4.00 5.00

u

Kx

(a)

(b)

Fig. 21. u versus Kx of plates with various plan aspect ratios D/B. (a) D=Bp1, (b) D=B41.


The best fit parameter with all data of plate models is: Cp ¼ 0:911 with a standarddeviation of s ¼ 0:0814. Cp can be regard as an average aerodynamic coefficient for platehorizontal trajectory. Thus for plates,

u � 1� e�ffiffiffiffiffiffiffiffiffi

1:8Kxp

; s ¼ 0:0814. (4)

Eq. (4) represents a good empirical prediction of the horizontal velocity of a plate when itreaches a given distance in a uniform wind flow.

0

1

2

3

4

5

6

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

#1 #2 #3 #4

#5 #6 #7 #8

#9 #10 #11 #12

#13 #14 #15 #16

#17 #18

0

1

2

3

4

5

6

#19 #20

#21 #22

Kx

Kx

Kt

Kt

(a)

(b)

Fig. 22. Kx versus Kt of plates with various plan aspect ratios D/B. (a) D=Bp1, (b) D/B41.


The data in Fig. 20 show that Kx is a polynomial function of Kt and can be expressed as

Kx ¼ 12CðKtÞ2 þ aðKtÞ3 þ bðKtÞ4 þ cðKtÞ5 þ � � � . (5)

The fitted expression,

Kx � 0:456ðKtÞ2 � 0:148ðKtÞ3 þ 0:024ðKtÞ4 � 0:0014ðKtÞ5 (6)

with s ¼ 0:134, can be used to estimate the horizontal travel distance of a plate at a givenflight time.It was noted that the scatter in the data were mainly from the data of the rectangular

plates with D=B41, which fell at relatively low wind speeds or flew highly at high windspeeds. The horizontal velocities of these plates decrease at the end of their trajectory dueto lower mean wind speeds in the wind-tunnel floor or ceiling boundary layers. In addition,these boundary layers will contain turbulence at scales that may influence the aerodynamicforces acting on the plates. Fig. 21 shows the data of u versus Kx for plates with D=Bp1and D=B41, respectively, and Fig. 22 shows Kx versus Kt.The characteristics of non-dimensional horizontal trajectories of compact and rod-like

debris [14] are comparable to those of plates, which indicate that functions (3) and (5), areapplicable to the other debris types. It was also observed that the contribution of thevertical component to resultant velocity was very small for plates, because the lift forcesustained the plate flight (Figs 23). Similar observations were drawn for rod-like debris.Compact debris experienced no lift force, fell in the experiments, and showed relativelylarge vertical velocity.

0

0.2

0.4

0.6

0.8

1

1.2

0.00 1.00 2.00 3.00 4.00 5.00

pla

te s

pee

d /

win

d s

pee

d

Horizontal speed

Resultant speed

Kx

Fig. 23. Comparison of horizontal and resultant velocities of plates.


4.4. Full-scale experiments

Full-scale test results showed flight behavior of plates comparable with that observed inthe wind-tunnel experiments, especially for the horizontal trajectories. Fig. 24 shows thetrajectory of plate model #17 (D=B ¼ 0:44, K ¼ 2.9) in a wind-tunnel experiment and thetrajectory of plate E1 (D/B ¼ 0.5, K ¼ 2.9) in a full-scale test. Full-scale plate E1 hadhigher trajectory than model plate #17 had, for the same K. Fig. 25 shows the horizontaland resultant speeds of plate #17 and those of plate E1. Fig. 26 compares all the horizontalplate trajectories in wind-tunnel experiments and full-scale tests (in semi-log scale).Relatively good agreement is obtained. The scatter evident at full scale is not unexpectedgiven the quite different launch mechanism and the decaying non-uniform flow behind theaircraft.

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 0.5 1.5 2 2.5 3Horizontal displacement (m)

Ver

tica

l dis

pla

cem

ent

(m)

0

1

2

3

4

5

6

0 10 15 20 25 30 35 40Horizontal displacement (m)

Ver

tica

l dis

pla

cem

ent

(m)

1

5

(a)

(b)

Fig. 24. Comparison of plate trajectories from wind-tunnel (above) and full-scale (below) tests. (a) Trajectory of

plate #17 (D/B ¼ 0.44, K ¼ 2.9, a0 ¼ 01), (b) trajectory of plate E1 (D/B ¼ 0.5, K ¼ 2.9, a0 ¼ 01).

ARTICLE IN PRESS

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8Time (sec)

pla

te s

pee

d /

win

d s

pee

d

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2Time (sec)

pla

te s

pee

d /

win

d s

pee

d

Um = ∆s / ∆t

Um = ds / dt

um = ∆s / ∆t

um = ds / dt

Um = ∆s / ∆t

Um = ds / dt

um = ∆s / ∆t

um = ds / dt

(a)

(b)

Fig. 25. Comparison of plate velocities from wind-tunnel (above) and full-scale (below) tests. (a) Non-

dimensional velocities of #17 (D/B ¼ 0.44, K ¼ 2.9, a0 ¼ 01), (b) non-dimensional velocities of E1 (D/B ¼ 0.5,

K ¼ 2.9, a0 ¼ 01).


5. Concluding remarks

Flight behavior of plate-type debris was extensively investigated in uniform wind-tunnelflow and in full-scale tests. The Tachikawa parameter K [8], side ratio D/B, and debrisinitial support configuration greatly affected plate trajectories in the vertical direction;however, K was the predominate influence on horizontal trajectories.The empirical equation (4) was derived based on extensive experimental data, and can be

used to estimate the plate speed at a given flight distance. It should be noted that debrismay have fallen to the ground before reaching the object of interest. Eq. (6) may be usedfirst to estimate potential travel distance of the plate at a given flight time. Plate flight timeis in the order of 1 or 2 s, as shown in full-scale tests (Fig. 25b). Potential flight times(before debris hits the ground) depend on the initial height of debris and the verticaltrajectory. Investigation of debris vertical trajectory is recommended for further research.This paper answers the questions of what plate travels at what horizontal speed, to what

distance. These data and derived empirical expressions have been reasonably confirmed by

ARTICLE IN PRESS

0

0.2

0.4

0.6

0.8

1

1.2

0.00 0.01 0.10 1.00 10.00

full-scale plates

model plates #1-#22

u − �u + �

u = 1 - e-√1.8Kx

u

Kx

Fig. 26. Comparison of plate horizontal trajectories from wind-tunnel and full-scale tests.

N. Lin et al. / J. Wind Eng. Ind. Aerodyn. 94 (2006) 51–76 75

full-scale tests, and may be employed in validating numerical models, as described in PartII [12].

The trajectories of compact objects (such as roof gravel) and rod-type objects (such asroofing members) and applications to impact test criteria are discussed in another paper[14].

Acknowledgments

This work was carried out under the US Department of Commerce TTU/NISTWindstorm Mitigation Initiative. The assistance of Mr. Taylor Gunn, Mr. Dejiang Chen,and Ms. Shannon Smith in carrying out all the experiments is gratefully acknowledged.Dr. Holmes was supported through the John P. Laborde endowed Chair at LouisianaState University and the LSU Sea Grant Program.

References

[1] J.A.B. Wills, B.E. Lee, T.A. Wyatt, A model of windborne debris damage, J. Wind Eng. Ind. Aerodyn. 90

(2002) 555–565.

[2] K.Y. Wang, C.W. Letchford, Flying debris behavior, in: Proceedings of the Eleventh International

Conference on Wind Engineering, Lubbock, TX, June 2–5, 2003, pp. 1663–1678.

[3] Experimental Building Station, Guidelines for evaluation of products for cyclone prone areas, Technical

Record 440, Experimental Building Station, Sydney, Australia, 1978.

[4] American Society for Testing Materials, Standard specifications for performance of exterior windows, glazed

curtain walls, doors and storm shutters impacted by windborne debris in hurricanes, ASTM E1996-03, 2003,

American Society for Testing Materials Inc., West Conshocken, Pennsylvania, USA, 2003.

[5] A.J.H. Lee, A general study of tornado-generated missiles, Nucl. Eng. Des. 30 (1974) 418–433.


[6] A.J.H. Lee, Trajectory of tornado missiles and the design parameters, in: Proceedings of the Second ASCE

Specialty Conference on Structural Design of Nuclear Plant Facilities, New Orleans, Louisiana, December

8–10, 1979.

[7] L.A. Twisdale, W.L. Dunn, T.L. Davis, Tornado missile transport analysis, Nucl. Eng. Des. 51 (1979)

295–308.

[8] M. Tachikawa, Trajectories of flat plates in uniform flow with application to wind-generated missiles,

J. Wind Eng. Ind. Aerodyn. 14 (1983) 443–453.

[9] M. Tachikawa, A method for estimating the distribution range of trajectories of wind-borne missiles, J. Wind

Eng. Ind. Aerodyn. 29 (1988) 175–184.

[10] J.D. Holmes, E.C. English, C.W. Letchford, Aerodynamic forces and moments on cubes and flat plates, with

applications to wind-borne debris. in: Fifth International Colloquium on Bluff-body Aerodynamics &

Applications, Ottawa, Canada, July 11–15, 2004.

[11] C.J. Baker, Solutions of the debris equations, in: Proceedings of the Sixth UK Conference on Wind

Engineering, Cranfield, September 15–17, 2004.

[12] J.D. Holmes, C.W. Letchford, N. Lin, Investigations of plate-type windborne debris, II. Computed

trajectories, J. Wind Eng. Ind. Aerodyn. 94 (2006) 21–39.

[13] C.W. Letchford, Analysis of the propeller wash from a C-130 Hercules aircraft, WISE Report for NIST,

August 2000, Texas Tech University.

[14] N. Lin, J.D. Holmes, C.W. Letchford, Trajectories of windborne debris and applications to impact testing,

J. Struct. Div- ASCE., accepted for publication.

lin_2006_journal-of-wind-engineering-and-industrial-aerodynamics.pdf

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