SIMULATION OF TORNADO-GENERATED MISSILES
by
DIA AREF MALAEB, B.S. IN C.E.
A THESIS
IN
CIVIL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
IN
CIVIL ENGINEERING
Approved
Accepted
,) December, 198()'
ACKNOWLEDGEMENTS
r. -·:' ._..,·!'I . ....-<-The author wishes to express his deep appreciation to Dr. James
R. McDonald for his patience, guidance and valuable assistance through
out this research effort. The support provided for the conduct of
this research by the Nuclear Regulatory Commission, by the Department
of Civil Engineering at Texas Tech University, and by the Institute
for Disaster Research at Texas Tech University is also acknowledged.
Drs. :<i shor C. Mehta and Joseph E. Minor are gratefully acknowledged
for their helpful criticisms and recommendations.
i i
CONTENTS
ACKNOWLEDGEMENTS
LIST OF TABLES
LIST OF FIGURES
I. INTRODUCTION
A. Objectives
B. Research Plan
II. REVIEW OF PREVIOUS RESEARCH
A. Previous Tornado Missile Trajectory Models
1. Wind Field Model
2. Aerodynamic Flight Parameter
3. Initial Conditions
4. Number of Degrees of Freedom
B. Basis for Rational Approach
1. Wind Field Model
2. Aerodynamic rlight Parameter
3. Initial Conditions
4. Number of Degrees of Freedom
C. Summary of Desired Trajectory Model Features
III. MISSILE TRAJECTORY MODEL
A. Wind Field r~odel
B. Missile Characteristics
C. Initial Conditions
D. Equations of Motion
i i i
Paoe ___..........,_
ii
v
vi
1
3
3
5
6
7
9
11
12
12
1 3
14
15
17
17
19
19
24
27
28
E . N wne r i c a l Sol u t ion
F. Computer Code
IV. COMPARISON OF SIMULATION STUDY WITH OBSERVED MISSILE BEHAVIOR
A. Approach
B. Bossier City Tornado
l. Damage Observations at Meadowview Elementary School
2. Fujita•s Analysis of Tornado Wind field
C. Factors Affecting Trajectory Path
D. Case Studies
1. Controlling Parameters
2. Trajectories Based on Fujita•s Analysis of Wind Fi~ld
E. Conclusions Based on Simulation Studies
V. SUMMARY AND CONCLUSIONS
A. Summary
B. Conclusions
LIST OF REFERENCES
iv
31
32
37
37
37
38
49
49
59
39
66
68
73
73
74
75
Table
1
2
3
4
5
6
7
8
9
LIST OF TABLES
Assumptions of Deterministic Missile Studies
Flow Chart of Computer Code
Summary of Missile Data
Fujita's Interpretation of Tornado Wind Field Data
Variation of Missile Velocities With Flight Parameter
Possible Values of Flight Parameter
Parameters Used for the Case Studies
Comparison of Observed and Calculated Impact Locations
Comparison of Observed and Calculated Impact Angles
v
Page
8
36
51
52
60
65
67
69
72
Figure
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
LIST OF FIGURES
Schematic Diagram of Single Vortex Tornado Model - DBT-77
Definition of Crossing Angle
Variation of Drag Coefficient with Orientation of Missile
Definition of Angles s and e
Tornado Damage in Vicinity of Meadowview Elementary School (Fujita, 1979)
Tornado Damage at Meadowview Elementary School
Typical Exterior Wall at Elementary School
Typical Beam-to-Column Connections at Roof
Roof Cross Section at Exterior Wall
Beam C Penetrated Eight Feet Irito Ground
Beam D With Pipe Column Still Attached
Beam D at Point of Impact After Passing Through Corner of House
Beam E With the Pipe Column Still Attached
Beam F Struck Roof of House Located 1000 Ft From School Building
Isovels of Tornadic Wind Speed as Interpreted By Fujita
Effect of Release Velocity on Missile Trajectory When Missile is Located to Left of Path
Effect of Release Velocity on ~issile Trajectory When Missile is Located to Right of Path
vi
21
23
26
29
39
40
42
43
44
46
46
47
48
48
50
54
56
LIST OF FIGURES (Cont'd.)
Figure
18 Missile Position Relative to Tornado Position When Missile is Released on Back Side of Tornado Core 57
19 Missile Position Relative to Tornado Position When Missile is Released on Front Side of Tornado Core 58
20 Variation of Missile Velocities With Values of Flight Parameters 61
21 Uplift Forces Required to Cause Column Anchorage Failure 63
22 Calculated Missile Trajectories and Observed Impact Points 70
vii
I. INTRODUCTION
The destructive damage caused by tornadoes in the United States
and in other countries such as Australia and Japan is receiving more
attention from engineers and managers each year. Responsible author-
ities are realizing that dollars invested in tornado protection pay
handsome dividends in safety, productivity, and damage mitigation
should that facility be struck by a tornado.
Damage caused by tornadoes is produced by three basic types of
forces:
1) wind induced forces,
2) atmospheric pressure change induced forces, and
3) impactive forces from windborne debris.
The research reported herein deals with the nature and characteristics
of the items picked up and transported by tornadic winds, i.e. tornado-
generated missiles.
Federal law* requires that structures that house equipment vital
to the safe shutdown of a nuclear power reactor shall be designed to
withstand the effects of natural phenomena, including tornadoes. The
spirit of this law has been applied to other facilities that
house nuclear materials, which, if released to the atmosphere, could
cause injury to people and damage to the environment. Such structures
*Policy and Regulatory Practice Governing the Siting of Nuclear Power Reactors [10 CFR Part 50].
must be designed to withstand certain types of potential missiles,
which are consistent with an acceptable risk level.
2
Hospitals, fire stations and conventional power plants should be
able to function after a tornado event. They, too, may require design
considerations for protection from tornado-generated missiles. Shel
ters for the protection of people in residences, schools and other
public buildings should also be designed to withstand impact from
tornado-generated missiles. Regardless of the degree of tornado pro
tection, the designer of a facility is faced with the so-called 11 tor
nado missile 11 problem. He needs to know the types of missiles that
are transported by tornadoes, their trajectory characteristics, and
the impactive effect on walls and the roof of his building. Thus, the
11 tornado mi ssil e 11 prob 1 em invo 1 ves the answer to four questions:
1) What types of missiles are transported by tornadoes?
2) How far do they travel?
3) How fast and how high do they go?
4) What type of barrier is needed to resist tornado-generated missile impact?
Tornado damage investigations give clues in answering the first
two questions. McDonald (1976) describes several types of missiles
that flew and some that did not. Generally, the types of missiles
transported by tornadoes range from very lightweight objects such as
roof gravel or sheet metal to very heavy objects such as pipes or
beams. The heaviest missile observed to date is a 40-ton railroad car
that was rolled and tumbled more than 200 yards in the Lillis, Kansas
3
tornado of 1978. (Incident is documented in tornado damage files of
the Institute for Disaster Research, Texas Tech University.) The dis-
tance traveled by a missile can be determined from field investigations,
provided its origin can be identified.
The answer to the third question is more difficult, since it is
almost impossible to obtain data on the missile trajectories themselves.
Photogrammetric analysis of movie films showing missile flights is one
possibility, but these films are rare. Indirect methods such as com-
puter simulation are the only alternatives available. Barrier analy-
sis and design involved with the fourth question are beyond the scope
of this project.
Objectives
The primary objectives of this research are to develop a rational
procedure for the simulation of tornado-generated missiles and to com
pare the results of the simulation with post-storm observations of
missiles that were transported by the Bossier City (Louisiana) tornado
of December 3, 1978.
Research Plan
The following research plan was developed and carried out in order
to accomplish the objectives set forth in this project:
1 )
2)
3)
Literature research and establishment of the need for a rational approach to tornado-generated missile simulation,
Development of the simulation methodology, and
Comparison of results from simulation with observed impact locations of Bossier City missiles.
4
Numerous attempts can be found in the literature to simulate or,
by some means, calculate tornado-generated missile trajectories.
Diverse results have been obtained because each researcher used a dif
ferent set of assumptions or conditions. Review of previous work is
presented with the objective of sorting out the different parameters
affecting trajectory characteristics. Once the various published
attempts at missile trajectory calculations are reviewed, the need for
a rational approach is obvious.
The simulation methodology involves selection of an appropriate
tornado wind field model, identification of significant missile char
acteristics, establishment of appropriate initial conditions, and
development of an appropriate computer code to perform the dynamic
trajectory calculations. •
A somewhat circumstantial approach to verification of the trajec
tory methodology is used. An attempt is made to simulate the trajec
tories of six steel wide flange beams that were transported by the
Bossier City tornado. Certain parameters relating to the tornado wind
field and missile characteristics are varied within a plausible range
to obtain trajectories that match the initial location and impact
position of the missiles.
II. REVIEW OF PREVIOUS RESEARCH
There have been numerous attempts to simulate tornado missile
trajectories. Almost all such efforts have been related to satisfying
licensing requirements for nuclear power plants. Other applications
of missile technology have been spinoffs from the nuclear power indus-
try.
To date, three basic approaches have used to gain an understand
ing of missile behavior:
1) a purely probabilistic, rather than deterministic, assessment of the missile problem;
2} Monte Carlo simulation of missile transport at a site specific location; and
3) establishment of a list of generic missiles by deterministic methods.
The first approach attempts to quantify the various probabilities
associated with an event that involves the occurrence of a tornado,
the presence of potential missiles in the tornado path, the accelera-
tion of the nissile to a velocity sufficient to cause damage, and the
impact of this missile at a critical point on the buiiding. To date,
no one has been able to quantify all of these probabilities to the
satisfaction of licensing authorities, although Meyer and Morrow (1975)
did try. Consideration of this approach is beyond the scope of this
research.
The second approach has not been used as a practical procedure
for design, but has been used as a research tool to study the missile
5
6
from a probabilistic point of view. Johnson and Abbott (1976) per
formed the equivalent of 10 million years of missile simulation by
passing randomly selected tornadoes over an idealization of the power
reactor site. All potential missiles were catalogued from an on-site
inspection. The computer code then calculated missile trajectories
as randomly selected tornadoes were passed over the site and recorded
strikes on the safety-related facilities. The probabilities of missile
strikes were then calculated. The amount of effort and computer time
required to generate the data is not practical for general design pur-
poses.
The third approach has been used by the NRC as a part of the
licensing procedure for nuclear power plants (Ref. NRC, 1975).
A list of generic missiles was somewhat arbitrarily selected by the
NRC licensing staff. Most previous work with tornado-generated mis
siles has been with the objective to prove or disprove the correct
ness of the NRC generic missile list. The list has been revised from
time to time, but still lacks justification based on a definitive
study of tornado missiles.
Previous Tornado Missile Trajectory Models
The methodology, including assumptions and calculation procedures,
is referred to herein as a missile trajectory model. Given certain
information about the tornado wind field and the missile characteris
tics, the model (usually in the form of a computer code) gives infor
mation about missile acceleration, velocity, and displacement as a
7
function of time. This type of model provides deterministic, rather
than probabilistic, information about the missile. Table 1 lists the
deterministic missile studies that have been conducted since the first
one was performed by Bates and Swanson in 1967.
The basic differences in the various models involve assumptions
regarding
1) \Jind field model,
2) flight parameter,
3) initial conditions, and
4) degrees of freedom of dynamic model.
The assumptions relating to the above four factors by each different
methodology are also given in Table 1.
Wind Field Model
Bates and Swanson (1967) used the analysis of Hoecker (1960) to
develop a wind field model of a tornado. The maximum wind speed of
the Dallas tornado was scaled to a value of 360 mph. Other methodol
ogies used slightly modified forms of the Bates and Swanson wind field
model (Paddleford, 1969; Lee, 1973; James, et al. 1974; Iotti, 1975).
The original Bates and Swanson model did not encompass all of space
around the tornado core. Later models identified wind flow in all of
space and established bounds on maximum tornadic windspeeds.
Bhattaharyya (1975) used a wind field model proposed by Kuo (1971).
While Kuo's model has a more rigorous fluid dynamic basis than the model
developed by Hoecker (1960), it is not convenient to use from an
TABL
E 1
ASSU
MPT
IONS
OF DETERMINI~TIC
MIS
SILE
STU
DIES
Win
d F
ield
Mod
el
Fli
ght
Para
met
er
Init
ial
De9
rees
0-
f R
efer
ence
Y
ear
Bas
ed O
n B
ased
On
Con
diti
ons
Free
dom
Date~ an
d Sw
anso
n 19
67
Hoe
cker
' s ~
lode
1
Eff
ecti
ve A
rea
Thr
ee
Inje
ctio
n 3
(Tum
blin
g)
Mod
es
Pad
dlef
ord
1969
H
oeck
er's
Mod
el E
ffec
tive
Are
a In
itia
l E
leva
tion
3
(Tum
blin
g)
Lee
1973
H
oeck
er's
Mod
el E
ffec
tive
Are
a Im
puls
ive
Inje
ctio
n 3
(Tum
blin
g)
Jam
es,
et a
l.
1974
H
oeck
er's
Mod
el E
ffec
tive
Are
a T
hree
In
ject
ion
3 (T
umbl
ing)
Oha
ttach
aryy
a 19
75
Kuo
' s M
odel
Max
i mum
Are
a (N
on-T
umbl
ing)
In
itia
l E
leva
tion
3
Iott
i 19
75
Hoe
cker
's M
odel
Eff
ecti
ve A
rea
Exp
losi
ve
Inje
ctio
n 3
(Tum
blin
g)
Bee
th a
nd
Hob
bs
1975
C
ombi
ned
Ran
kine
E
ffec
tive
Val
ue
Init
ial
Ele
vati
on
3 V
orte
x (T
urub
ling)
Mey
er a
nd
Mor
row
19
7S
Com
bine
d R
anki
ne
Eff
ecti
ve V
alue
In
itia
l E
leva
tion
3
Vor
tex
(Tum
blin
g)
Sirn
iu a
nd
Cor
des
1976
C~nbined
Ran
kine
E
ffec
tive
Val
ue
Init
ial
Ele
vati
on
3 V
ol'te
x (T
ulftb
ling
)
Red
man
n,
et a
l,
1976
EP
RI
Mod
el A
vera
ge
Val
ue
Var
ious
In
itia
l 3
(Tum
blin
g)
Ele
vati
ons
& P
osit
ions
Red
man
n,
et a
1.
197B
EP
RI
Nad
el
Act
ual
Val
ue
Var
ious
In
itia
l 6
Ele
vati
ons
& P
osit
ions
00
•
engineering standpoint. Other methodologies use a combined Rankine
vortex assumption for the variation of tangential wind speed (Beeth
and Hobbs, 1975; Meyer and Morrow, 1975; Simiu and Cordes, 1976).
Simple relationships for radial and vertical wind speed components
were assumed which do not satisfy continuity of flow.
Redmann, et al. (1976) developed a wind field model that was
based on data, experiments and photographs of tornadoes. The major
restriction on the model, which is consistent with equation of fluid
9
dynamics and continuity, is an arbitrary limitation of 225 mph on the
tangential wind speed.
Aerodynamic Flight Parameter
The drag force F that acts on the missile due to the resultant
wind vector is given by
where
( l )
p is the mass density of air
c0
is a drag coefficient that is a function of the missile shape, surface roughness and Reynolds number (in some cases)
V is the net resultant wind velocity vector
A is the area (or equivalent area) of the missile exposed to the wind vector
The missile acceleration due to the force of the wind is
F -a = m
where
m is the mass of the missile
y is pg, the unit weight of air
W is the missile weight
10
Thus, one measure of the missile acceleration is the so-called missile
flight parameter c0A;W.
If a body (missile) is streamlined and if no flow separation
occurs, it may behave like an airfoil, i.e. there is a lifting force
associated with horizontal flow. Most typical tornado missile shapes,
however, do not behave as an airfoil and thus are lifted only by the
vertical component of the wind field. None of the methodologies des
cribed in Table 1 consider the effect of a lift force.
An issue associated with the flight parameter that has sparked
considerable debate is the question of whether a missile rolls and
tumbles during flight along its trajectory, or whether it assumes some
invariant position relative to the resultant wind vector. The tumbling
or nontumbling issue affects the value of c0A used in the flight param
eter. Both the drag coefficient and the area could be different for
all objects, except spheres. In general, the methodologies have util
ized expressions for an equivalent area, which is supposed to account
for the effect of tumbling. All methods except Lee (1973) and
Bhattacharyya (1975) assume the tumbling mode. Each method uses a
different expression for equivalent area.
The missile weight does not appear to be a problem, if one is
considering the trajectory of a bare element such as a pipe, a beam,
11
or a pole. However, missiles generated by a real tornado are rarely
11 Clean, 11 but have other elements or pieces of deoris attached to them
for all or part of the missile flight. This situation affects values
c0, A, and W in an unmeasurable way. Thus, a more realistic and
manageable approach to trajectory calculation may be to consider
ranges of values of the flight parameter and not worry about individ
ual values of c0, A or W.
Initial Conditions
Bates and Swanson (_1967), in their original \'/Ork, discussed three
modes of tornado missile injection into the wind field: ramp, explos5va,
and aerodynamic lift. Ramp injection, according to their perception,
is possible when a missile first rolls or tumbles up an incline and
then becomes airborne. This injection mode is site dependent. The
explosive mode is associated with the effect of a rapid atmospheric
pressure change in a tornado. Recent research (Minor and Mehta, 1979)
discounts an explosive mode of failure due to atmospheric pressure
change for most ordinary buildings. Lee (1973) proposed an initial
impulse force that acted on the missile for a short period of time.
Associated with a coefficient of lift, the missile becomes airborne in
Lee's scheme if the lift force is sufficient to overcome the gravita
tional force of the object.
Most other approaches have simply placed the missile at some
arbitrary location relative to the tornado path and at some arbitrary
elevation above ground level. The tornadic winds are then allowed to
suddenly take effect. Parametric studies are performed to find the
12
location that produces the worst case relative to velocity achieved
and distance traveled by the missile. The missiles are released at
different elevations above ground, up to 200 ft. This approach is
taken because potential missiles could be located atop tall structures
during construction at a power plant site, and partly to give the
tornadic winds sufficient time to act on the missile before it impacts
with the ground.
Number of Degrees of Freedom
All methodologies except the one by Redmann, et al. (1978) consider
the missile as a point mass and treat the dynamic problem as one with
three degrees of freedom rather than six, which is the most general
case.
The diverse approaches to tornado missile trajectory calculations
and the diverse results obtained from these approaches suggest the need
to establish a rational approach based on the best and most logical
features of previous methodologies as well as new innovations.
Basis for Rational Approach
From review of previous work on missile trajectory calculations,
the following conclusions are reached regarding the various assumptions
required for a rational method of analysis:
1 )
2)
None of the wind field models used previously are sufficiently rigorous, have reasonable bounds, and yet are simple enough for engineering applications.
Possible variations of the elements of the aerodynamics flight parameters (c0, A and W) make it difficult to precisely define each one individually.
13
3) Missile injection into the wind field is not realistic and does not account for the anchorage forces resisting missile movement.
4) In light of our present knowledge of drag and lift coefficients for various types of missiles and the attachments they may have during flight, the three-degree-of-freedom dynamic model appears to be adequate for trajectory calculations.
5) None of the previously proposed methodologies have been used in an attempt to match missile behavior observed in an actual tornado.
The tornado missile trajectory model presented in this report
attempts to satisfy the requirements for a rational approach that is
consistent with technology as we presently know it.
Wind Field Model
Redmann, et al. (1976) provides an excellent critique of the
interpretation of Hoecker's analysis of the Dallas tornado. Attempts
to generalize the Dallas model for other tornadoes entails extrapolating
scaling relationships which have little or no physical basis. There is
no attempt to tie the results to basic fluid mechanic equations of
motion and continuity. Use of a combined Rankine vortex in lieu of the
Hoecker analysis for tangential wind variation is a justifiable simpli
fication. However, the models that use the combined Rankine vortex
have other deficiencies similar to those that use Hoecker's analysis.
The Kuo model is rigorous from a fluid dynamic point of view.
However, physical parameters required in the solution of the equations
are not easily defined. The model proposed by Redmann, et al. (1976)
has the rigor and the simplicity needed for engineering analysis. Un
necessary bounds on maximum wind speeds and an attempt to force the
14
model to satisfy (and justify) the so-called Tephigram method of bounds
on the potential intensity of a tornado renders the model less than
desirable for practical applications of missile trajectory calculations
for power plant licensing purposes.
The single vortex wind field model proposed by Fujita (1978) (as
opposed to his multiple vortex model) appears to satisfy most, if not
all, of the model defficiencies cited above; yet, it is simple enough
for engineering calculations. Designated DBT-77 (Design Basic Tornado
based on 1977 technology), the model is based on photogrammetric anal-
ysis of tornado movie films and on damage patterns observed in post-
storm investigations. Fluid mechanics equation of motion and continuity
are generally satisfied, and scaling parameters for adjusting the tor
nado size (radius of maximum wind speed) are consistent and have a
physical basis. The model is described in detail in Chapter III.
Aerodynamic Flight Parameter
Selection of the proper value for the aerodynamic flight param-
eter provides a series of contradictory problems.
1)
2)
3)
Missiles are rarely 11 Cl ean 11; they have attachments that affect
values of CD' A and W.
While a tumbling mode seems intuitively correct, there is evidence from tornado damage patterns that long slender missiles such as pipes, poles and beams tend to align themselves in the same direction.
The majority of long slender missiles impact 11 0n-end. 11 This position is inconsistent with the assumption that the maximum area of the missile aligns itself normal to the wind velocity vector.
These inconsistencies lead to the conclusion that precise values
of the aerodynamic flight parameter cannot be defined. Earlier attempts
15
to define equivalent area (Bates and Swanson, 1967; Beeth and Hobbs,
1975; Simiu and Cordes, 1976) are merely rationalization for reducing
the exposed area without any real physical basis (e.g. wind tunnel
tests). Therefore, the approach proposed herein is to consider reason
able ranges of values of flight parameters rather than attempts to
define specific values of c0, A and W. Upper bounds are obtained by
taking the largest values of c0 and A, but these may not be reasonable.
The effects of varying the flight parameter over a certain range is
illustrated in Chapter IV in association with the Bossier City tornado
missiles.
Initial Conditions
As defined, initial conditions apply to the conditions at the
missile prior to being affected by the tornaGo. The three initial
conditions are initial height, initial location relative to tornado
path, and missile release velocity Vmr· Observations of post-storm
damage indicate that objects lying loose on the ground or even at
some elevation above ground are rately (if ever) transported by the
wind. McDonald (1976) observed that utility poles that were stacked
on a rack five ft above ground were not transported by the Brandenburg,
Kentucky tornado of April 3, 1974. The poles were located in an ideal
position to be transported by one of the most intense tornadoes that
has ever occurred in the United States. Stacks of pipes, electrical
transformers and other types of loose objects were also not picked up.
Thus, it appears that some type of sudden release of an object is
16
required for it to be injected into the wind field. Such a release can
occur due to the sudden failure of connections or anchorages, by roof
uplift or wall collapse. Sudden release of the resisting forces pro
vided by anchors has the effect of an instantaneously applied force.
This force then accelerates the missile and moves it into position to
be affected by the drag force components of the wind.
In the trajectory model proposed herein, each missile type has an
associated missile release velocity V , which is the wind speed mr required to overcome the anchorage forces that resist movement of the
missile by the tornadic winds. The missile release velocity has a
significant effect on the path taken by the missile.
the missile may not be transported at all.
I f V i s sma 11 , mr
Since most missile shapes are not airfoils, the only uplift is
due to the vertical component of the wind field. A missile lying on
the ground will never be picked up if the vertical wind component is
zero at ground level, as it should be. A ramp-type injection as
perceived by Bates and Swanson (1967) is possible, if the missile
rolls and tumbles up a ramp and is lifted above the zero ground datum.
The above statements are consistent with observations of post-storm
damage. In the Brandenburg tornado, the winds blew past high stacks
of lumber. The. top boards were blown off of the stacks and some were
transported more than two miles. However, as the height of the stacks
decreased, they finally reached a level where no more boards ~Ere
picked up, indicating that when the stacks reached a certain level, the
vertical component of the wind was not able to sustain them in the wind
field.
17
The initial location of the missile relative to the tornado path
has two effects. If the missile is too far removed from the path, the
missile release velocity Vmr will never be reached, and the missile
will not be transported. The location of the missile relative to the
tornado path at Vmr also affects the path taken by the missile.
Number of Degrees of Freedom
While the six-degree-of-freedom approach taken by Redmann, et al.
(1978) is the most rigorous (it's hard to imagine a 12-in. dia pipe,
16ft long as a point mass), the variation of drag and lift coeffi-
cients as a function of missile attitude are not known. In the Redmann,
et al. study, a limited number of objects (12-in. dia pipe and auto
mobile) were tested full scale in a wind tunnel to obtain data on the
variation of the drag and lift coefficients. When the results of the
three-degree-of-freedom model and the six-degree-of-freedom model were
compared, they were not terribly different, although the six-degree-of
freedom model predicts slightly lower missile velocities.
Summary of Desired Trajectory Model Features
Based on review of previous attempts at tornado-generated missile
trajectory calculations, the following are judged to be the most
desirable features of a trajectory model:
1 )
2)
3)
Wind field model: DBT-77 by Fujita
Aerodynamic flight parameter: Use a range of values rather than specific values of CD, A and W.
Dynamic Model: Three degrees of freedom with a step-by-step numerical integration scheme.
4) Initial Conditions: Consider initial height above ground, initial location of missile relative to tornado path, and missile release velocity.
These features are described in detail in the next chapter.
18
III. MISSILE TRAJECTORY MODEL
The methodology, including the assumptions and the calculation
procedures, is referred to as the missile trajectory model. If cer
tain initial conditions about the tornado and the missile are speci
fied, the model gives information about the accelerations, the
velocities, and the displacements of the missile as a function of time.
The characteristics of the wind field model can also be changed as a
function of time.
Details of the trajectory model, along with assumptions and cal
culation procedures, are described in this chapter.
Wind Field Model
The assumptions and limitations on wind field models used previ
ously are discussed in Chapter II. The model that seems to best satis
fy requirements of rigor and simplicity is the single vortex model
proposed by Fujita (1978). This model, designated as DBT-77*, was
developed by Fujita as a design basis tornado in 1977 for use by engi
neers in the design and evaluation of structures. The model was
developed from the many observations of tornado damage and from photo
grammetric analysis of tornado movies. The wind field model satisfies
the basic laws of fluid dynamics, including continuity of flow.
*For fur the r i n format i on on 0 B T- 7 7 , see F u j i t a (J 9 7 8 ) ~
19
20
A schematic diagram of the single vortex wind model, DBT-77, is
shown in Figure l. The model is an axis-symmetrical vortex with a
cylindrical core. The core is divided into two parts: an inner core
with rad~us Rn, and an outer core with radius R0
. Vertical motions are
confined to the outer core. The inner core contains a region of rota
tional flow surrounded by the outer core which contains irrotational
flow.
The inflow layer has a height H., where air feeds into the outer l
core of the tornado and then flows vertically upward. Above the inflow
layer, the flow is outward.
The tangential velocity component in this model is expressed as the
product of two functions, each of which varies with height and radius.
The tangential velocity is given by
V = Flr) F(h) Vm (3)
where Vm is the maximum tangential wind speed; F(r) and F(h) are identi
fied as radial and height functions, respectively. They are given by
F ( r) =
~~~~ ~ F(h) =
r 1/r hko e-k(h-1)
( r < 1 )
~h: n (4)
(h > l)
where rand hare the normalized radius and the normalized height, res-
pectively, at which the tangential wind speed is calcualted. Values of
k0
and k are assumed to be l/6 and 0.03 in this model. Fujita (1978)
states that as more observational data are accumulated in the future,
the values of k0
and k may change slightly.
MAXIML'M TANGENTIAL VELOCITY, Vm~
I I
I ,; ~·· if.·'.; .· +t.:
I
I I
I I
I I
I
;.-INNER i COREJ OUTFLOW
J ' 1 '
----.. J ____ _ ~ )
OUTER CeRE
21
FIGURE l. SCHEMATIC DIAGRAM OF SINGLE VORTEX TORNADO MODEL- DBT-77
22
The radial wind speed is expressed in this model by
U = V tan a (5)
where a is the crossing angle, which denotes the angle between the
direction of the incoming air flow and a concentric circle of radius r
at their crossover point (See Figure 2). In this model, a is assumed
to be zero inside the inner core. It increases or decreases outward
within the outer core, reaching a0
at its outer edge. Outside the
core, a0
remains constant everywhere. The value of a is expressed by 0
= -A (1-h312) m
= B (1-e-k(h-1)) m
inside inflow layer (6)
outside inflow layer
where Am and Bm are positive nondimensional quantities called the
11 maximum inflow tangent 11 and the 11 maximum outflow tangent,11 respectively.
The vertical velocity component inside the inner core and outside
the outer core is assumed to be zero. Inside the outer core, the ver-
tical velocity is assumed to be horizontally uniform and may be expressed
by
w = w v o m where w is the normalized vertical velocity expressed by
0
w0
= 0.398[2e-k(h-l)]
(7)
(8)
In summary, the DBT-77 tornado wind field is completely defined if
three parameters are specified: Vm, R0
and Vt (the translational speed
of the tornado). The three components of wind velocity can be normalized
with respect to Vm. The normalized wind speeds are
u = U/V o m v0 = V/Vm w0 = W/Vm
(9)
0 < R < Rn
Rr'l < R < R0
R0 < R
Qt..= 0
0 < o<. ( =<.0
<><.-~ - 0
~ I '
( 0( =-o )
/ /
FIGURE 2. DEFINITION OF CROSSING ANGLE
23
At inflow heights (where h < 1)
uo = -A hl/6(1-h3/2) m
vo = hl/6
wo = 3/28 EA (16h7/ 6 - 7h8/ 3) m
where E = 0.55 and A = 0.75 are used in this model. m
At outflow heights (where h > 1)
where k1 = k(h-1 ).
u0
= 27/28 k ~ (e-kl - e-2ki)
vo = e-kl
w 0
= 2 7 I 2 8 E Am ( 2 e- k 1 - e-2 k 1 )
At the top of the inflow layer (where h = 1)
u = 0 0
vo = 1
w0
= 27/28 E Am
24
( 1 0)
( 11)
( 12)
The values of Vm' R0
and Vt can be varied with time, if appropriate.
With these three quantities defined at any time t, the three wind field
components, u , v , and w0
can be defined for any point in space. 0 0
Missile Characteristics
Whenever an object is placed in a moving fluid (or moves through a
stationary fluid, as is the case with misssiles), it will experience a
force in the direction of motion of the fluid relative to the object
(drag force) and it may experience a force normal to the flow direction
(lift force). Drag and lift forces are caused by the sum of the tangen
tial and normal forces at the surface of a body. Drag due to tangential
stresses is called friction or viscous drag. Drag due to normal
stresses is called pressure drag. It is usually dominant on bluff
bodies. Drag coefficients must be experimentally determined, and
they generally depend on Reynolds number. Drag coefficients of
shapes typical of tornado-generated missiles are summarized in
Hughes and Brighton (1967). Drag coefficients for additional
shapes, including the wide flange beam section, are given in
Heorner (1958).
If the missile traveled in a fixed attitude, then the area
normal to the flow, or the projected area, would be the appropriate
value to use in the drag force equation. However, because of the
questions relating to whether a missile tumbles or not, there is
25
no precise expression for area available. The ma~imum area gives an
upper bound value and is conservative but is not necessarily realis
tic. Not only does the area change from one side of the missile to
the other, but the drag coefficient may also change, as illustrated
in Figure 3.
If there are appendages or attachments to the missile during
flight, these also change the value of area. In a similar manner,
they also increase the weight, as well as the coefficient of drag,
of the missile.
Thus, because of the unknown factors in the c0, A and W terms
of the flight parameter, the trajectory model is set up to deal with
OB
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EFFI
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ITH
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OF M
ISSI
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! I I
N
0'\
27
one value of flight parameter rather than considering individual values
of all three parameters. It is necessary then to determine what range
of values the flight parameter can assume using reasonable variations
of c0, A and w. Initial Conditions
Three initial conditions affect the missile trajectory:
l) initial height above ground,
2) missile release velocity, and
3) location of missile relative to tornado path.
The trajectory model can handle a wide range of values for the three
parameters. The initial height above ground affects the value of the
vertical wind component which produces the only upward acting force on
the missile. Typical missile shapes are not airfoils and thus there
is no lift force, per se. The missile release velocity greatly affects
the path taken by the missile and determines to some extent if the mis
sile will move at all. If the missile release velocity is greater than
the wind speed that occurs at the missile location, the missile remains
stationary. If the release velocity is small, the missile does not
experience a large initial acceleration and may not travel very far.
The missile release velocity can be calculated if its anchorage strength
is known or can be estimated (Mehta, et al., 1976). Because of uncer
tainties of material strength, a range of V may have to be considered. mr The trajectory model assumes that the missile is at some fixed
location and the tornado translates past the missile. When the tornadic
28
wind speed at the missile location exceeds V , the missile begins to mr move. Otherwise, it remains stationary.
Appropriate values for initial missile height, V and initial mr location must be chosen consistent with conditions at the site in
question.
Equations of Motion
The equations of motion used in this study are based on a rectan-
gular coordinate system. The three wind components U, V, and t~ (the
radial, the tangential, and the vertical wind speed, respectively) are
converted to rectangular coordinates by the following transformation
equations:
v = X
u cos e- v sine
vy = u sine+ v cos e ( 13)
vz = w
where Vx and VY are the horizontal wind speeds in the x and y direc~ons,
respectively. V2
is the vertical wind speed in the z direction, and e
is the angle that the line joining the tornado center and the missile
position makes with the x-axis (See Fig. 4).
The translational wind speed is resolved into an x component and a
y component and added vectorially to Vx and Vy, respectively
vt = vt cos s X
vt = vt sin s y
( 14)
where vt is the translational velocity of the tornado, vtx and vtyare
0
I
/
TORNADO WINDS
M!SSILE L..CC!.TION
L-------------------------------------------------------1
FIGURE 4. DEFirliTION OF ANGLES B and e
29
30
its components in the x and y directions, respectively, and s is the
angle between the tornado path and the x-axis.
The force acting upon the missile due to the action of wind is
given by
F = l/2pC0V~ .ll, (15)
where p is the mass density of the airflow; p = .00237 slug/ft3 at stan
dard temperature and pressure
A is the area (or equivalent area) of the missile in ft2
c0 is the coefficient of drag of the missile (unitless)
Vr is the magnitude of the relative wind vector in ft/sec.
Using Newton 1 S second law of motion, this force is divided by the mass
of the missile to obtain the missile acceleration
F C0pV~A a = M = 2m
which reduces to
a = o. s (c0A/W) y v~
( 1 6)
( 17)
where m is the mass of the missile, W is the weight of the missile in
pounds, andy is the density of air which is equal to 0.76411 lb/ft3
at
standard temperature and pressure.
Now, introducing
P f = c0 A/W ( 18)
where Pf is recognized as the aerodynamic flight parameter of the
missile. Equation (16) reduces to 2
a= 0.5yPfVr ( 1 9)
31
the acceleration is also calculated in three directions using the fol
lowing relations:
a.x = 0.5 p f-v v r.x r
ay = 0.5 P fv v ry r (20)
az = 0.5 P fv v rz r
where ax, ay' and az are the missile accelerations in the x, y and z
directions, respectively.
The terms V , V and Vrz are the relative wind velocities in the rx ry
x, y and z directions, respectively, and are defined by
v = vx v rx 1TIX
v = v v (21) ry y my
v = v vm r- z z z
where~ , V and ~ are the missile velocities in the x, y and z mx my mz
directions, respectively. The wind vector, Vr, is then defined by
(22)
Numerical Solution
Most researchers expressed the motion of the missile by a set of
ordinary differential equations of the first order. They integrated
these differential equations forward in time from prescribed initial
conditions to the point of impact of the missile. In this study, an
iterative scheme of simulation is developed to numerically solve the
missile propagation problem. A computer program is written based on
32
this iterative approach. It is assumed that the acceleration a between
any two points varies linearly with time so that
(23)
where dt represents the time interval between point i and point i+l, and
K is a constant which is initially assumed to be
K= (a.- a. 1)/dt
1 1- (24)
Then, based on this assumption, the new velocity and position of the
missile at point i + 1 are evaluated by the following equations:
VM = 0.5 (a.+ a.+1)dt + VM i+ 1 1 1 J•li
(25)
and
RM = 0.5(V. + V.+l) dt + RM i+l 1 1
(26)
where RM is the position of the missile with respect to the origin of
the coordinate axes.
Once the new position and velocity of the missile are known, the
acceleration of the missile due to the wind field can be calcualted
using Equation (20). Using the new value of the acceleration at point
i+l, the process is repeated until the acceleration at point i+l are
within some specified tolerance e.
Computer Code
To calculate and plot trajectories and velocities of tornado
generated missiles, a computer program was developed. The program was
written in FORTRAN language to numerically solve the equations formulated
in the previous sections of this chapter. The program calculates the
missile position, velocity and acceleration as a function of time.
33
The only input data required for the program are the tornado wind
field characteristics, the missile characteristics, and initial condi
tions. The use of Fujita's DBT-77 as the wind field model simplifies
the formulation of the wind distribution. Only three tornado oarameters
are required as input. These are the maximum tangential wind speed, the
outer core radius, and the translational speed of the tornado. These
quantities may be constant, or they may vary with time. The path of the
tornado is also required as input to the program.
The missile characteristics include the weight, the coefficient of
drag, and the area of the missile. These may be entered separately as
c0, A, and W, respectively, or in one value (C0A/W) which is the flight
parameter of the missile.
The initial conditions of the missile include the initial height,
the initial location (with respect to a specified coordinate system),
and the missile release velocity.
The tornado wind field data covers a certain period of time. The
data is recorded at each specific time interval for the whole duration
of the tornado. These time intervals are divided into small time
intervals (a l/10 sec. time interval is used in this study). The wind
field data is then calculated at each step, or time interval, by a
linear interpolation between each two original consecutive intervals.
For example, the wind field data of the Bossier City tornado was
recorded every two seconds of·the tornado duration. The total duration
was 46 seconds (23 data set intervals). The program calculates, by
linear interpolation, the wind field data every l/10 sec., i.e., at
34
460 time steps. The use of a very small time step interval leads to
more accurate results, but it requires more computational time.
The code consists of a main program and four subroutines. The
input data is entered in the main program. The four subroutines are
called LINE, WINVEL, ACCEL and PLOT.
Subroutine LINE uses the given path data and generates intermediate
path data. The number of data points desired is controlled by an arbi
trarily chosen spacing or time interval. A linear interpolation scheme
is used.
Subroutine WINVEL is the tornado wind field model based on Fujita•s
OBT-77. It calculates the tangential, radial and vertical wind speeds
at any desired point. In this case, the desired point is the missile
position at each time step. A transformation of these velocities from
polar to rectangular coordinates is performed at the end of the sub
routine.
Subroutine ACCEL calculates the acceleration of the missile due to
the resultant wind vector that acts on the missile. This acceleration
is also calculated in the x, y and z directions.
The last subroutine, PLOT, plots the trajectory taken by the
missile from the point of release to the point of impact.
After reading the tornado path data and the missile characteris
tics and initial conditions, the program calls LINE and generates a
desired number of intermediate path data. ThenWINVEL is called and
the wind speed at the missile initial location is calculated. This
35
step is repeated until the resultant wind speed at the missile location
reaches the missile release velocity previously defined in the program.
At this point, the missile is no longer stationary. Subroutine ACCEL
is then called and the acceleration of the missile due to the net wind
speed is calculated. The program then calculates the new position of
the missile and repeats the above steps until the missile hits the
ground. The maximum horizontal velocity, vertical velocity, and height
attained by the missile are estimated. Then, subroutine PLOT is called
and the trajectory is plotted if desired.
The program prints out, at every calculation step, the position of
the tornado, the wind speed ~nd the missile•s x, y and z positions.
Then, it prints out the extreme values of the missile acceleration,
horizontal velocity, vertical velocity and height. A flow chart illus
trating the program is shown in Table 2.
TABLE 2
FLOW CHART OF COMPUTER CODE
Read tn:
Tornado Path Data: tornado position, mutmum t•nqentrar veloclty, outer core radius, translational soeed.
Mi!Sile Characteri~tlcs: initial locatrO'ii';iiilT\41vel~coefficient of drag, weight, area, release veloci ~y.
Ca 11 LINE:
Calculate Intermediate Path Data at selecte~ n .. nber of steps or tjrne interva 1 s.
Call WHlVEL:
Determine the step at which the wind speed at the missile Initial location reaches the predetermined miss! le release velocity.
I
Ca 11 ACCEL:
Calculate the nfsslle acceleration due to the resultant wind vector ac~ ing on the missile.
1 Calculate the missile po~itton and velocity at that step, then ca 11 '.I!NVEL. ' =
>---~_j Calculate missile extremes: ~..1<imum horizontal velocity, m.uimum vertical velocity, maxfmu"l height,
write out: ~t each ~tc.2.:., tornado posttio~, wind speed in x, y and z directrons, mtssrle velocltres in x, y and z direction.
After impact: maximum mtss1le acceleration, maxrmum horTzontal velocity, maximum verticil velocity, mHimum height.
Ca 11 PLOT: Plot the trajectory, if desired.
36
IV. COMPARISON OF SIMULATION STUDY WITH OBSERVED MISSILE BEHAVIOR
One of the main objectives of the missile study is to compare the
results obtained from the missile trajectory model developed herein
with some observed missile behavior. Missile trajectory calculations
are presented to show that the computer simulation can give a reason
able approximation to the actual missile trajectories, at least to the
point of matching the initial missile location and the final position
of the missile impact.
Approach
The approach taken in this study was to treat the wind field
characteristics of the Bossier City tornado, as deduced by Or. Fujita
from the damage arid debris patterns, as known quantities. The advan-
tage of this approach is that it eliminates some of the unknowns
associated with the problem. The only variables, then, are related to
the missile itself. The missile parameters were systematically varied
until a set of trajectories were obtained that matched the impact
points of the six wide flange beams that were transported by the Bossier
City tornado. Details of the calculations described above are presented
in subsequent sections of this chapter.
Bossier City Tornado
On the night of December 3, 1978, a devastating tornado struck
Bossier City, Louisiana cutting a six mile path through the city. Two
people were killed, houses, commercial business and public buildings
were damaged or destroyed. The tornado damage was documented by a
37
38
team of researchers under sponsorship of the U.S. Nuclear Regulatory
Commission. Team members included Dr. J. R. McDonald from Texas Tech
University, Dr. T. T. Fujita from the University of Chicago, and R. F.
Abbey, Jr. from the NRC. The tornado event was meticulously documented
by means of aerial and ground level photographs, surveys and interviews
with eye witnesses to the storm. Dr. Fujita subsequently analyzed the
damage and deduced his interpretation of the tornado event. Of parti
cular interest was the tornado-generated missiles found at the
Meadowview Elementary School.
Damage Observations at Meadowview Elementary School
Figure 5 shows a plot plan of the school and the neighborhood
surrounding it. From aerial photos taken shortly after the tornado, •
the extent of damage to residences and the school have been plotted
on the drawing. Debris patterns are also shown on the drawing. The
x-y coordinate axes give an indication of the scale.
Also shown in Figure 5 are the impact locations of the six steel
wide flange beams that were transported by the tornado. The beams
were 14 in. deep, 24 ft long and weighed 30 lbs per ft (AISC designa
tion: W14x30). The beams supported the roof of the southeast wing of
the school. They spanned in an east-west direction along the top of
the south exterior wall. Figure 6 shows a general view, looking
*This drawing was prepared by Or. T. T. Fujita.
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nt G~ASS
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ri)
Wfl
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ES
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TS
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AH
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ST
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-.--:
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u /
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A----------------------~
50
0
10
00
15
00
20
00
2
50
0
FIGU
RE
5.
TORN
ADO
DAMA
GE
IN
VIC
INIT
Y O
F ME
ADOW
VIEW
ELE
MEN
TARY
SCH
OOL
(FW
JITA
, 19
79)
w
1.0
_J
0 0 ::c u C./)
>-0::: c:r: 1-z: L.I..J :E: L.I..J _J L.I..J
3 l.J....I ....... > 3 0 0 c:r: l.J....I :E:
1-c:r: l.J....I ~ < :E: c:r: 0
0 a c:r: z 0::: 0 I-
40
41
northeast, of the damage to the school building. The southeast wing
(wing nearest bottom of photo) received the most extensive damage.
The south wall has collapsed and the roof is missing from one third
of the wing area. Other wings of the building have broken windows
and some roof removal, but there are no other collapsed walls.
Figure 7 shows an elevation of one of the exterior walls that
did not collapse. It is constructed similar to the south wall. There
is a buttress which has no structural value and an overhang of approxi
mately four ft. The wide flange beams provided continuous support of
the roof along the entire length of the wall.
The beams were supported by pipe columns at approximately 24 ft
on center in a manner similar to that shown in Figure 8. The beams
were bolted or welded to the column cap plates. Knee braces made of
2 x 1~ x ~angles were located at each column. Fi~ure 9 shows a
typical cross section at the exterior wall. Open web steel joists
rested on the top flange of the Wl4x30 beams. Each joist was welded
to the beam with two 1/4 in. welds, 1 in. long. The top chord of the
joists extended approximately four ft beyond the beam and supported
the roof overhang. The roof was constructed with 2 1/2 in. light-
weight concrete over corrigated metal deck. A built up tar and gravel
roof completes the roof system.
The pipe columns had a 6x6 base plate that was anchored to the
foundation with 2 3/4 in. dia anchor bolts. Instead of using nuts
_J
0 0 :c u (/)
>-0::: c:I: tz LL.J ::E: LL.J _J LL.J
tc:I: _J _J
c:I: 3
0::: 0 -0::: LL.J t>< LL.J
_J
c:I: u -c.... >t-
. """ LL.J 0::: ::::> (.!:) -u..
42
LL... 0 0 ~
1-c::(
t/)
z 0 ......... 1-u LL.J z z 0 u
z :a: :::::> .....J 0 u
I 0 I-
I :a: c::( LL.J co .....J c::( u ......... c... >-1-
. 00
LL.J 0::: :::::> ~ -LL...
43
!1'-
lo"
8.0
12
14
MA
T·,
~2\:i.r_~~-==
COLU
MN
-·o
~ + ···-_
. '!'"_
'b
FIGU
RE
9.
ROOF
CRO
SS S
ECTI
ON A
T EX
TERI
OR W
ALL
0:
•.,J ~ +
COLU
MN
+::>
+::>
45
on the anchor bolts, as is customary, the bolts were burned off flush
with the top of the base plate and then were welded to the plate.
The impact points of the six beams (_designated A through F) are
shown in Figure 5. The precise location of each beam along the top
of the wall could not be determined. The two beams designated A and
B impacted the ground fairly close to the building, although subse
quent trajectory calculations suggest that they may have traveled in
a large loop before hitting the ground. Beam A struck the ground on
end, but had been removed from the ground before a depth of penetration
could be measured. It is not known if beam B landed on-end or not.
Beam C is shown in Figure 10. This beam struck the ground with suffi
cient force to penetrate 8 ft into the ground. It is located about
400 ft from the southeast corner of the wing from which it came. Beam
Dis shown in Figure 11. It still has a pipe column attached to it.
The impact point was across the street from where it is shown in the
figure. It passed through the corner of the house shown in Figure 12
and then penetrated into the ground. A couple was sleeping in a bed
located in the same corner where the beam came through. Fortunately,
the beam passed above them and they were not injured. Beam E landed
in the open school yard (See Fig. 13). The column attached to the
beam was apparently bent prior to impact. The base plate, which is
similar to the one shown in Figure 12, was still attached to the end
of the column. The si~th beam, Beam F, impacted the furthermost dis
tance from the school. It struck the roof of the house shown in
46
FIGURE 10. BEAM C PENETRATED EIGHT FEET INTO GROUND
•
FIGURE 11. BEAM D WITH PIPE COLUMN STILL ATTACHED
FIGU
RE 1
2.
BEAM
D A
T PO
INT
OF
IMPA
CT A
FTER
PA
SSIN
G TH
ROUG
H CO
RNER
OF
HOUS
E
~
""'-~
FIGURE 13. BEAM E WITH THE PIPE COLUMN STILL ATTACHED
FIGURE 14. BEAM F STRUCK ROOF OF HOUSE LOCATED 1000 FT FROM SCHOOL BUILDING
48
49
in Figure 14~ traveling in a direction from east to west. Fortunately,
no one in the house was hurt from the impact of this beam.
All of the beams except possibly Beam B impacted on-end. Table 3
gives information on impact locations and angles of impact. It is
significant that the beams impacted on-end. While the evidence is
somewhat circumstantial, it indicates that missiles of this type may
travel in some fixed relationship to the resultant wind vector.
Fujita·~ Analysis of Tornado Wind Field
By interpretation of damage and debris patterns, Fujita estimated
the location of the center line of the tornado path as it traveled
across the school area. In adiditon, he deduced values of the outer
core radius R0
, the maximum tangential wind speed, and the transla
tional speed of the tornado as it traveled along the path. These
values are tabulated in Table 4. The interpretation of the tornadic
wind speeds in the form of isovels is given in Figure 15. The maximum
wind speed in the area where the wide flange beams ~~re located was
estimated to be 200 mph. Note from Table 4 that the outer core radius
as the tornado passed over the school is less than 50 ft. This is an
extremely tight core tornado as interpreted by Dr. Fujita, and has a
significant effect on the trajectories taken by the missiles.
Factors Affecting Trajectory Path
Before describing the trajectory calculations needed to match
the Bossier City missile impact points, a brief discussion is presented
fu...
\ I
\
50
(/) c::(
a LLJ LLJ Cl.. (./')
a z ........ ::s: u ........ a c::( z 0:::
,-., 0 5 1-Q l..J...
0
0
(/)
.....J LLJ > 0 (/) ........
51
TABLE 3
SUMMARY OF MISSILE DATA
Initial Location a Im12act Locationa ImQact Angle
Missile X y X y Horizontalb Verticalc
" 1200 920 1375 .-1 945 N 50° E Unknown
B 1224 920 1410 915 N 85° E 30°
c 1245 920 1590 700 s 30° E 23°
D 1266 920 1780 940 s 60° E 20°
E 1290 920 1535 1400 N 20° w so
F 1311 920 1450 1710 N 80° w Unknown
NOTES:
a. Coordinates are referenced to Figure 5.
b. Bearing angles are based on direction missile was traveling at impact.
c. Angle is measured from the horizontal ground plane.
52
TABLE 4
FUJITA'S INTERPRETATION OF TORNADO WIND FIELD DATA
Outer Core Maximum Translat1onal Path Coordinatesa Time Radius Tangent i a 1 Velocity
(sec) X ( ft) y (ft) (ft) (mph) (mph)
0 0 0 43 141 40
2 75 90 46 135 40
4 145 185 49 128 40
6 220 280 66 122 39
8 300 385 89 "117 37
10 375 495 135 114 34
12 450 620 190 112 30
14 520 700 230 111 27
16 585 745 236 110 25
18 675 820 233 111 32
20 835 870 190 116 43
22 1000 875 105 131 47
24 1145 910 59 155 44
26 1255 945 46 175 40
28 1360 1010 49 175 38
30 1455 1080 59 167 35
32 1535 1160 89 155 32
34 1605 1230 105 150 30
36 1715 1295 82 150 36
38 1855 1310 52 158 45
40 1965 1380 43 170 42
42 2055 1460 46 170 38
44 2150 1540 56 155 37
46 2245 1600 72 140 35
a. Coordinates are referenced to Figure 5.
53
on those factors that most significantly affect the missile trajectories.
The ones treated as variables in this study were
1) initial conditions, and
2) flight parameter.
The three initial conditions are initial height of missile, initial
location and missile release velocity. The initial height was treated
as a constant (15ft above ground level). The other two are somewhat
interrelated.
In these calculations, the missiles are located at some fixed
point, and the tornado is passed by along a predetermined path. The
missile is not free to move until the tornadic wind speed reaches the
missile release velocity. The missile trajectory can take a variety
of paths, depending on where the missile is located and what the mis
sile release velocity is. Consider two cases:
l) missile located to left of tornado path, and
2) missile located to right of tornado path.
If the missile is located to the left of the path, Figure 16 shows
that it can be picked up at the front of the tornadic winds at point A
or at the rear at point B, because of the influence of the translational
speed of the tornado. Thus, if the missile release velocity is less
than the resultant wind speed at A, the missile will be released at A
and will follow a path as indicated in Figure 16. If the release veloc
ity is greater than the wind speed at A, but less than or equal to the
wind speed at B, the missile will be released at B and will take a
"' ' \ MISSILE TRAJECTORY
\ ( V m r < v, a < V r b )
v \ \
\' Nra \ ~ RESULTANT WINC '/::LOCITY
~ / /':I!A-- V t
/U ------+-~~~~~~//~------~-------------~ORNADO
'-/1- ;'"' PATH
RESULT;l,NT 'NINO VEL'JC!TY
" Vrb "
V - Tangential Velocity U - Radial Velocity
' ' ' " ...........
Vt - Translational Velocity of Tornado
"':t. MISSILE 7?AJECTORY (V <V (V )
ra mr ro
Vra' Vrb- Resultant Wind Velocity at A & 8, Respectively
54
FIGURE 16. EFFECT OF RELEASE VELOCITY ON MISSILE TRAJECTORY WHEN MISSILE IS LOCATED TO LEFT OF PATH
•
totally different path. If the release velocity of the missile is
greater than the resultant wind speed at both points A and B, then
the missile will not be picked up. A similar situation occurs if
55
the missile is located to the right of the tornado path (See Fig. 17).
After the release of the missile from its anchorage, its path
depends on the missiles position relative to the wind field. Two
cases are illustrated, In Figure 18, the missile is located on the
left side of the tornado path. The release velocity is such that the
missile initially moves under influence of winds on the back side of
the tornado core. In this case, ~he missile travels along the tornado
path and remains ahead of the tornado center. Finally, it crosses the
tornado path and strikes the ground.
The missile in Figure 19 is located in the reight side of the
tornado path and is released on the front side of the tornado core.
It crosses the tornado path and is then affected by the tornadic winds
on the back side of the core. This causes the missile to make a loop.
While the missile is making the loop, the tornado moves away from it.
The net distance traveled by the missile from its point of origin is
generally small, compared to the previous example. However, the dis
tance traveled along the trajectory path may be quite large.
Because the flight parameter is directly proportional to the accel
eration of the missile under the influence of the wind forces, it
affects the maximum horizontal velocity, the maximum vertical velocity,
the maximum height achieved, and the distance traveled from its
original location.
" MISSILE TR AJEC"T'ORY
\ ( vrc < vmr < vrd )
I I I I
.,....-+-~Vrc ---r--------~------~~~------~TORNAOO
PATf-l
V - Tangential Velocity
U - Radial Velocity
Vr - Translational Velocity
7RA,jECTORY
{ Vrc < Vmr < V;d )
Vrc' Vrd - Resultant Wind Velocity
Vmr - Missile Release Velocity
FIGURE 17. EFFECT OF RELEASE VELOCITY ON MISSILE TRAJECTORY WHEN MISSILE IS LOCATED TO RIGHT OF PATH
56
/
/
19
MIS
SIL
E
IMP
AC
T
TO
RN
AD
O
/TO
RN
AD
O
CORE
--------
-----
~ '- ',
"~
FIGU
RE 1
8.
MIS
SILE
PO
SITI
ON
RELA
TIVE
TO
TORN
ADO
POSI
TION
WHE
N M
ISSI
LE
IS R
ELEA
SED
ON
BACK
SID
E OF
TOR
NADO
COR
E
4
MIS
SIL
E
PO
SIT
ION
Ul
........
MIS
SIL
E
---
' 7
'6'~ '-
--M
ISS
ILE
IM
PA
CT
FIGU
RE
19.
MIS
SILE
PO
SITI
ON
RELA
TIVE
TO
TORN
ADO
POSI
TION
WH
EN M
ISSI
LE
IS R
ELEA
SED
ON
FRON
T SI
DE
OF
TORN
ADO
CORE
I
Ul
00
59
Table 5 illustrates the effect of flight parameter on the trajectory
characteristics. The initial conditions are such that the trajectory
is similar to the one in Figure 18. The percentage of maximum tangential
velocity versus flight parameter is plotted in Figure 20 for the maximum
horizontal and vertical velocity achieved by the missile under a specific
set of wind field and initial missile conditions. Increasing the value
of flight parameter above some value (0.05 in this case) has little
· additional effect on the maximum horizontal and vertical velocities.
Objects with small value of flight parameter are more sensitive than
the ones with large values. Thus, when examining a possible range of
values for flight parameter, it is sensitive to the magnitude of the
flight parameter itself.
Case Studies
The case studies described in the general approach are presented
in this section. The tornado wind field data deduced by Or. Fujita
are used in the simulation. The parameters that control the paths and
impact locations of the six wide flange beam missiles are discussed
first. These include the initial conditions and the flight parameters.
Controlling Parameters
An initial height above ground of 15 ft was assumed for all cases
studied. The location of each missile relative to the tornado path is
obtained from the damage analysis. Using Fujita's interpretation of
the wind field, the path location is given in Table 4. The initial
location of the missiles is atop the south wall of the southeast wing of
the school. Precise initial locations are found in Table 3.
TABLE 5
VARIATION OF MISSILE VELOCITIES WITH FLIGHT PARAMETER*
Flight Maximum Maximum Maximum Parameter Horiz. Vel. Vert. Ve 1. Height J ft2 I 1 b) (ft/sec) (ft/sec) (ft)
. 01 38.5 28.5 15.0
. 02 96.6 37.3 23.9
. 03 135. 9 54.4 51.1
. 04 164. 0 62.9 81.5
. 05 178.9 65.9 98.2
.06 188.4 66.3 102. 7
. 07 194.3 67.4 103.5
. 08 199. 7 . 72.3 111.9 •.
. 09 204.4 75.9 118.4
. 10 208.7 78.6 123.2
. 11 212.6 80.6 126.7
. 12 216.0 81.8 129.2
. 13 219.3 82.6 130.8
. 14 222.1 82.9 131. 7
. 15 225.0 82.9 132.0
*Missile Initial Conditions:
Initial Height: 15 ft Initial Location: On center line of tornado path Release Velocity: 200 mph
Tornado Parameters: · Maximum Tangential Velocity, Vm: 200 mph
Translational Velocity: 50 mph Outer Core Radius: 50 ft
60
Maximum Dist. Traveled
(ft)
33
127
426 653
755 786 789 827 857
872
885 893 892
890 895
100
) t- 0 0
80
_. w
>
_. ~
t- ~
60
(!
) z ~ ~ ~
::! 4
0
x ~ :1
\L
0 w !i'
20
t z w
0 a:
w
ll.
C)
N
0 d
\10~~
~~_;J~-
•
MA
XIM
UM
V
E.R
!II,
./\L
Y
LL
Y"'
._y _
__
__
__
__
_ _
-
'¢
10
CD
Q
0 0
0 d
0 F
LIG
HT
P
AR
'AM
E T
ER
Q
d N
0 • 0
!!?
0 CD
0 0 N
0
FIGU
RE
20.
VARI
ATIO
N OF
MIS
SILE
VE
LOCI
TIES
WIT
H VA
LUES
OF
FLIG
HT
PARA
MET
ER
0'\
__
,
62
The range of missile release velocities considered was obtained by
analyzing the wind speed required to cause uplift of the beams. The
critical wind load acting on the roof is shown in Figure 21. The term
p is the wind pressure in psf. The dead load of the roof is 37 psf 0
(see Fig. 21). For a one ft wide strip of roof, the following expres-
s ion for the anchorage resistance R can be obtai ned by writing a sum
mation of moments about point 0.
R = 28.7p0
693 (lb/ft) (27)
The columns are spaced at 24 ft on center. The perimeter of a 3/4 in.
dia anchor bolt is 2.36 in. Therefore, since the weld resistance per
in. on two bolts is 14.38 k/in. (see Fig. 21), we can write from
Equation (23):
(_14.28)(2.36) =(28.7p0
- 693) (28)
Solving for p0
,
p = 72.9 psf (29) 0
The corresponding wind speed in mph is obtained from the equation
2 p0
= 0. 00256V ( 30)
Therefore, the wind speed is
'1 = /p /0. 00256 ·o
= 169 mph
( 31 )
Similar calculations show that the column anchorage is the weakest link
in the system. This finding is verified by observations in the field.
63
. TTTJifl l !I I ll ~~ ~ f"lT~ /
{/f
COLUMNS SPACED ~ 24'-o"
Ar-1 -.A R
UPLIFT FORCES
Roof Load: Tar & gravel Lightweight concrete Steel joists Ceiling
5.5 16/ft2 27.0 3.4 1.0
36.9 l6/ft2
2-~;4' o A. SOL ~s
( 1/4" WC:LD AROUND BOLT PERIMETER l
SECTION A-A
Note: Joist-to-beam and beam-to-column connections are stronger than column anchorage.
Weld Resistance (E70 Electrodes) Rw = l/4(0.707)(40.4)(2)
= l4.28k/in. (based on ultimate shear strength)
FIGURE 21. UPLIFT FORCES REQUIRED TO CAUSE COLUMN ANCHORAGE FAILURE
The value of Y = 169 mph represents an idealized situation. If
less weld were used, of if there were defects in the weld or missing
welds, failure could occur at wind speeds less than this value. On
the other hand, unaccounted strength or additional dead weight could
cause the wind speed to produce failure higher than the calculated
value. The range of values used in the trajectory calculations was
130-190 mph.
64
Since the proposed approach involves assuming values of flight
parameter rather than individual values of c0, A and W, the first step
was to determine what a reasonable range of values might be. Table 6
lists a number of possible values of the flight parameter based on
various values for c0, A and W.
Since the most likely failure mode involves uplift of the entire
roof, subsequent to failure at the columns anchor bolts, it seems likely
that the beams were initially attached to sections of the roof during
their flights. These roof sections could be of various sizes, depending
on how the roof came apart. The basic dead load of the roof was 37
lb/ft2. However, parts of the roofing material could have come off
prior to column anchorage failure, so the roof might have weighed con
siderably less than the 37 psf, depending on the situation. As the
size of the roof section increases, its drag coefficient is likely to
decrease. For flat plates, with wind blowing normal to the surface,
the value of c0
varies from 1.2 to 1.95, depending on the length to
width ratio. As the value decreases, the values approach 1.2. The
TABL
E 6
POSS
IBLE
VA
LUES
OF
FL
IGH
T PA
RAM
ETER
=
Mis
sile
N
et
Roo
f D
eck
Wei
ght,
psf
,
Beam
plu
s 2
5 10
20
x-
sq f
t o
f CD
pf
~~
p f
pf
roof
dec
k A
w
w
w
----
0 2
.0
28
720
. 078
72
0 .0
78
720
.078
72
0
50
1.8
78
82
0 . 1
71
920
. 145
12
20
.115
17
20
100
1.6
12
8 92
0 .2
23
1220
. 1
68
1720
. 1
19
2720
200
1.4
228
1120
.2
85
1720
. 1
86
2720
.1
17
4720
400
1.2
428
1520
. 3
38
2720
. 1
89
4720
. 1
09
8720
600
1.2
628
1920
.3
93
3720
.2
03
6720
. 1
12
1272
0
800
1.2
82
8 23
20
.428
47
20
.211
87
20
. 114
16
720
30
pf
w
.078
72
0
. 082
22
20
. 075
37
20
. 068
67
20
.059
127
20
.059
187
20
.059
24
720
pf
w
.078
72
0
.063
25
20
.055
44
20
.048
81
20
.040
155
20
.040
229
20
.040
303
20 37
pf
.078
.055
.046
.039
.033
.033
.033
())
U1
66
beam alone has a CD that varies from 1.0 to 2.0, depending on orienta
tion about the longitudinal axis. Thus, it appears to be reasonable
that as additional sq ft of roof area is added to the beam, the value
of CD should decrease from a maximum of 2.0 down to 1.2.
From Table 6, it is found that the range of values of flight
parameter goes from 0.033 to 0.428. The values to the right of the
solid line appear to be the most plausible ones. It does not seem
likely that a large surface area would be present that would have a
very light weight per sq ft. Thus, a more reasonable range of values
is 0.033 to 0.28.
Trajectories Based on Fujita's Analysis of Wind Field
The trajectory calculations are based on Fujita's interpretation
of the Bossier City tornado. The wind field parameters are listed in
Table 4. The objective is to perform a series of trajectory calcula-
tions and determine the set of parameters that will give trajectories
that match the impact points of the Bossier City tornado missiles.
The two parameters that were varied were missile release velocity and
flight parameter. Table 7 shows the combination of parameters that
were used in this study. A total of 80 cases were examined. The
flight parameters needed to obtain the match ranged from 0.03 to 0.28.
The missile release velocity ranged from 95 mph to 150 mph.
The results of each of the 80 trajectory calculations were
examined (six trajectories; one for each missile are obtained for each
case study). The case that best matched the impact point for each
67
TABLE 7
PARAMETERS USED FOR THE CASE STUDIES
Flight Parameter
{ psf) . 03 .033 . 035 . 050 . 100 . 150 .200 .250 .260 .280
l gl 1* 2 3 4 5 6 7 8 9 10
~I n 12 13 14 15 16 17 18 19 20 +->
~~ 21 .,...
22 23 24 25 26 27 28 29 30 u 0
..-
~I 31 OJ 32 33 34 35 36 37 38 39 40 > OJ
~141 V1 42 43 44 45 46 47 48 49 50 1'0 OJ
,....-
~~51 OJ 52 53 54 55 56 57 58 59 60 0:::
OJ
~161 ..- 62 63 64 65 66 67 68 69 70 .,... V1 V1 .,...
~171 72 73 74 75 76 77 78 79 80 :::E:
*Case Number
68
individual missile was selected and tabulated in Table 8. The trajec
tories are referred to as trajectories 1 to 6. The observed impact
points are labeled A to F. The coordinates of the observed impact
points and the calculated impact points and the errors are listed in
the table. Except for impact point E, the calculated points are
remarkably close. Figure 22 shows a horizontal olot of the 6 trajec
tories and the locations of the impact points.
Conclusions Based in Simulation Studies
Upon examination of values of missile release velocity and flight
parameters that were required to match the observed locations of all
six missiles, the following is observed:
1) The missile release velocities are relatively lovJ, compared to the calculated "ideal" release velocity of 170 mph.
2) Three of the six missiles required flight parameters that are near the lower limit of the acceptable range, and the other three required flight parameters that are near the upper limit.
3) While the impact points of the missiles match very well, the observed angles of impact do not match the calculated ones very well.
The justification of the low release velocities that were required
to match the observed impact location is that the tornadic winds might
have lifted parts of the roofing material prior to the release of the
missiles from their anchorage. This might have reduced the resistance
of the column release R, and hence the release velocity, Vmr
Because the beams were located along the top of the 140 ft wall,
they are not expected to have the same·values of flight parameter and
pf
v T
raje
ctor
y m
r N
umbe
r (f
Ulb
) (m
ph}
1 .2
60
95
2 .0
35
100
3 . 0
30
150
4 .2
80
100
5 .0
33
100
6 . 2
00
105
TABL
E 8
COM
PARI
SON
OF O
BSER
VED
AND
CALC
ULAT
ED
IMPA
CT L
OCAT
IONS
Max
. H
oriz
. M
ax.
Ver
t.
Max
imum
-O
bser
ved
-ta 1
cul a
ted
Ve1
ocit
) V
eloc
ity
Hei
ght
Imna
ct
Impa
ct
(fti
_sec
..
( ft/
sec)
_
(ft)
x(
f_tl
· y
( ft)
~{
ft)
y(f
t)
231
82
238
1450
17
10
1468
17
67
108
35
24
1410
91
5 14
11
916
145
45
54
1780
94
0 17
40
972
204
82
361
1535
14
00
1310
14
55
71
33
18
1375
94
5 13
85
944
144
61
189
1590
70
0 15
96
694
Mis
sile
M
atch
ed
F
B c E
A
D
Err
or
{ft
)
60 1 51
232 10
8
0'\
lO
ft
1700
1600
,_
1500
1400
·-
/E
Ele
men
tary
S
cho
ol
1300
1200
·-
1100
·-
1000
900
·-
300
700
·-~6
600
ft
1000
JJ
OO
12
00
JJO
Q
]4Q
Q
•rn
n
•·--
FIGU
RE
22.
CALC
ULAT
ED M
ISSI
LE T
RAJE
CTOR
IES
AND
OBSE
RVED
IM
PACT
PO
INTS
.....
._. 0
71
release velocity. Each would have more or less amounts of roof attached
and the anchorage failure resistance would be slightly variable.
The flight parameters required to match the observed impact loca
tions are all within the reasonable range defined earlier. The ~issiles
that did not travel very far (missiles A, B and D) are the ones that
required low flight parameters. Those that traveled long distances
(missiles C, E and F) are the ones that required high flight parameters.
A comparison between the observed and the calculated angles of
impact is shown in Table 9. Only three of the trajectories (trajec
tories l, 2 and 5) gave a very close match of the observed angles. Also
shown in Table 9 are the calculated impact velocities of the missiles.
Unfortunately, soil samples were not taken at the time of the tornado,
so the physical properties of the soil are not known. However, the
calculated impact velocities shown in the table suggest that the impacts
observed are feasible.
Missile
A
B
c
D
E
F
TABLE 9
COMPARISON OF OBSERVED AND CALCULATED IMPACT ANGLES
Observed Calculated ImQact Angle ImQact Angle
Horizontal Vertical Horizontal Vert1cal
N 50° E Unknown N 60° E 15°
N 85° E 30° N 85° E 15°
s 30° E Z3° N 70° E zoo
s 60° E 20° s 70° E 16°
N zoo w so s 80° E 4Z 0
N 85° W Unknown s 60° w 43°
7Z
Calculated Impact
Velocity
11 3 ft/ sec
79 ft/sec
150 ft/sec
153 ft/sec
7Z ft/sec
61 ft/sec
V. SUMMARY AND CONCLUSIONS
Summary
In this study, a rational approach for the simulation of tornado
generated missile trajectories has been presented. A wind field model
that is practical and has a physical basis is utilized in the formula
tion of a three-degree-of-freedom trajectory model that is realistic
and practical from an engineering point of view. The trajectory model
calculates the position, velocity, and acceleration of the missile as
functions of time. The model is capable of handling tornadoes with
parameters that vary with time. These parameters include the path,
the maximum tangential wind speed, the outer core radius, and the trans
lationa1 speed of the tornado.
The missile characteristics required for the trajectory simulation
are the initial conditions, the release velocity, and the flight param
eter. The initial conditions include the initial elevation and the
location of the missile relative to the tornado path. The release
velocity depends on the anchorage of the object to the structure and
the resistance of the structure to the wind-induced pressure. The
flight parameter can be calculated as a function of the drag coefficient,
area and weight of the missile. It can be accurately calculated for
bare missiles, but in the case where the missile has appendages or
attachments of unknown weight and area, the flight parameter varies
within a certain range and cannot be assigned a specific value.
73
74
Conclusions
The following conclusions on the trajectory simulation model and
the comparison of calculated missile behavior with observed missile
behavior are made:
1. A missile is sustained by the tornadic winds if a sudden
release is applied on it. As the missile release velocity
increases, the initial acceleration of the missile due to
the tornadic winds increases; hence, the missile travels
faster, higher, and further than one released at low wind
speeds.
2. Since mis-sfles are rarely "clean, 11 a range for the flight
parameter, rather than specific values of the coefficient of
drag, the area and the weight, is suggested.
3. The calculated impact locations of the six wide flange beam
missiles transported by the Bossier City tornado match very
closely with the observed ones; the calculated angles of
impact do not match the observed angles as well; and the
impact velocities resulting from the simulation are of
sufficient magnitude to cause the missiles to penetrate the
ground as observed.
LIST OF REFERENCES
Bates, F.C., and Swanson, A. E., ~lovember, 1967. 11 Tornado Design Consideration for ~iuclear Pov.1er Plants," The American Nuc~ear Society, ~nnual Meeting, Chicago, Illinois.
Beeth, D.R., and Hobbs, S.H., October, 1975. ''Analysis of Tornado-Generated Missiles," Topical Keport S&R-001.
Bhattacharyya, A.:<., 3oritz, R.C., and ~liyogi, P.K., October, 1975. ''Characteristics of Tornado-Generated Missiles," United '::ngineers, Inc., Philadelphia, Pennsylvania.
Fujita, T.T., September, 1978. "Workbook of Tornadoes and High Winds for Engineer-ing .:1.pplications," University of Chicago, S~!RP Research Paper 165, Chicago, Illinois.
Fujita, T.T., January, 1979. "Preliminary Report of the Bossier City Tornado of December 3, 1978," Department of Geophysical Sciences, University of Chicago, Chicago, Illinois.
Hoecker, W.H., Jr., Hay, 1960. "J.Jind Speed and ,-\ir Flow Patterns in the Jallas Tornado of .1\pril 2,"1957 ," Monthly '1Jeather Revie•.-J, Vol. 88, :lo. 5, pp. 167-180.
Heorner, S.F., 1965. "Fluid Dynamic Drag," Hoerner Fluid Dyna:nics, Sri ck T m~m, New Jersey.
Hughs, ~i.F., and Brighton, J.A., 1967. "Theory and Problems of :=luid Dynamics," Scham' s Outline Series, McGraw-Hill Book Compc.ny.
Iotti, R.C., June, 1975. "Design Basis Velocities of Tornado Genen~ed Missiles," Paper Presented at Annual Conference of American Nuclear Society, New Orleans, Louisiana.
James, R.A., Burdette, E.G., and Sun, C., November, 1974. "The Generation of Missiles by Tornadoes, 11 Tennessee Valley Authority, TVA- TR74-l.
Johnson, T., and Abbot, G., November, 1977. "Simulation of Tornado Missile Hazards to the Pilorim 2 Nuclear Thermal Generating Station,'' Science ,0-,pplications, Inc., Bechtel Power Corp., San Francisco, California.
Kuo, H. L. , January, 1971. "Assymmetr~ c Fl m•:s in the Sound a ry Layer of a Maintained Vortex,'~ Journal of Atmosoheric Sciences, Vol. 28 No. 1.
75
76
Lee, A.J.H., December, 1973. "A Study of Tornado Generated Missiles," ASCE Specialty Conference on Structural Design of Nuclear Power Plant Facilities, Chicago, Illinois.
McDonald, J.R., June, 1976. "Tornado-Generated Missiles and Their Effects," Symposium on Tornadoes: Assessment of Knowledae and Implications for Man, Texas Tech University, Lubbock: Texas.
Mehta, K.C., Minor, J.E., and McDonald, J.R., September, 1976. "Windspeed Analyses of April 3-4, 1974 Tornadoes, 11 Journal of the Structural Division, ASCE, Vol. 102, No. ST9.
Meyer, B.L., and Morrow, W.M., June, 1975. "Tornado Missile Risk Model," Bechtel Power Corpo_ration, San Francisco, California.
Minor, J.E., and Mehta, K.C., November, 1979. "Wind Damage Observations and Implications," Journal of the Structural Division, ASCE, Vol. 105, No. STll.
NRC, 1975. "Missiles Generated by Natural Phenomena," U.S. Nuclear Regulatory Commission, Standard Review Plan, Revision 1, Office of Nuclear Reactor Regulation, Washington, D.C.
Paddleford, D. F., April, 1969. "Characteristics of Tornado Generated Missiles, Nuclear Energy System, Westinghouse Electric Corporation, WCAP-7897.
Redmann, G. H., Radbill, J.R,, Marte, J.E., Dergarabedian, P., and Fendell, F.E., February, 1976. "Wind Field and Trajectory Mode 1 s for Tornado Prope 11 ed Objects,'' El ectri ca 1 Power Research Institute, Technical Report l, Palo Alto, California.
Simiu, E., and Cordes, M., April, 1976. 11 Tornado Borne ~1issile Speeds," Institute for Basic Standards, National Bureau of Standards, prepared for the U.S. NRC, Washington, D.C.
