where @ is measured relative to the horizontal. Since, for the present, the impact and
rebound angles are assumed to be equal, the vertical and horizontal components of
rebound velocity are

<
"

ev,
“ . (9)

The vertical component of rebound velocity can be used to compute the time to second
impact by .

te Ve (10)

and the horizontal travel distance to second impact is given by

2
-vite 2e°v, Vv, (11)
g

hr

where g is the acceleration due to gravity.
7.2 Horizontal Bounce Distance

At low impact velocities, the energy (and hence velocity) lost in deforming an impacting
body and scarring the surface is relatively small, leading to a coefficient of restitution
somewhat higher than that for high-velocity impacts. For iron on iron, lead on lead, and
iron on lead, approximate values of e®! within some unspecified (but surely low)
velocity domain are 0.66, 0.20, and 0.14, respectively. During an inelastic impact where
the impacted body is relatively large and at rest, the kinetic energy (KE) lost by the
falling body can be obtained by multiplying the KE at impact by (1 - e’). If a value of
0.4 is used for e, 84% of the impact KE is lost and 16% remains to produce bounce. If
e=0.2, 4% of the energy produces bounce. As a numerical example, consider a
100-pound piece impacting with a vertical velocity component of 20.9 ft/sec,
(W/C,A = 0.5 lb/ft’), and a horizontal (wind) velocity of 11.5 ft/sec. If e = 0.4, 16% of
the impact KE produces a rebound velocity of 9.5 ft/sec. The rebound angle is 61.2°,
and the impact range is 2.4 feet. Table 4 shows bounce distances for six values of e and
nine ballistic coefficients, assuming a horizontal velocity component at impact of 11.5
ft/sec, and a vertical velocity component equal to terminal velocity computed as follows:

‘April 13, 1995 13


The probability that the center of the splatter fragment impacts in interval i can be found
by integrating the density function f(r) over the interval. Since f(r) is a straight line, the
same result is obtained by multiplying the height of the density function at r = r, by the
interval width. Using Eq. (33),

Prob (:) = 2(mm ~ 5) y (36)

r
‘max

For the i" interval, the effective casualty area is obtained by multiplying the probability
of impacting in the interval [Eq. (36)] by the area swept out by the projected fragment
[Eq. (34)]. The total effective area for the fragment is the sum for all such intervals i.
With the restriction that the trajectory for the projected fragment does not rise above h,
feet, the conditional effective casualty area for a single projected fragment can thus be
written as follows:

A, (no overflight)

i]
a
N
Bae
3
+
4
a
wt
1
4
on
+
NI
$
+
on
—_
se

max 7)

. tn) Y bn - olf Hy) + Thea? a

ist
max

8.5 Elimination of No-Overflight Restriction

The restriction on trajectory height will now be removed to allow for the possibility that
the projected fragment may overfly a vulnerable individual. Some speculation is
involved since there is no way to know what trajectory a fragment flies in reaching a
particular impact range. In view of this uncertainty, corrections to the conditional
effective casualty area are made using vacuum calculations and a flat, non-rotating,
constant-gravity earth.

Figure 12 depicts the trajectory of a flat circular fragment that is projected above height
h, before impacting at distance r, from the origin. Throughout flight the fragment plane
is assumed to be horizontal.

April 13, 1995 34


8. Splattering and Cratering

If an inert vehicle piece or component impacts in an open area, piece fragments or
chunks of the impacted surface may be forcefully projected away from the periphery of
the falling piece. Such projected fragments may pose a significant risk to people nearby.
For high-velocity impacts on hard surfaces such as rock, concrete, and blacktop, piece
fragments and surface chunks may be thrown outward considerable distances. For
impacts on soft surfaces such as lawns, fields, roadsides, and sandy beaches, splattering
and cratering hazards will be considerably reduced. For low-velocity impacts, the
kinetic energy may be insufficient to produce either splattering or cratering, although the
possibility of bounce or skid still exists. .

Although some experimental data pertaining to cratering and fragment projection from
explosive charges are available in the literature, little or no similar data exist for-
inert-piece impacts, insofar as can be determined. Thus, in modeling such events, the
analyst is largely left to his own resourcefulness and imagination. Claims of rigor and
precision cannot be made for such modeling. Still, splattering and cratering phenomena
exist in the real world, so even a speculative model should be superior to no model at
all.

In estimating casualty area due to splatter, both hard and soft surfaces are considered.
Except for the functions used to define the maximum splatter range and the number of
splatter fragments, the procedures and equations for the two surfaces are identical. In
making risk calculations for people in the open, the type of surface on which each
person or group of people is located must be specified. If the type is unknown or not
indicated, the assumption is made that the surface is hard.

8.1 Basic Assumptions

With the above caveats in mind, the following basic assumptions have been made in
modeling splattering and cratering effects from inert impacts. Specific assumptions
about the number of splatter fragments produced, and the maximum range to which
fragments are projected, are provided later:

a. Splatter fragments are thrown radially outward from the boundary of the
impacting piece, with all directions being equally likely.

b. Impacting vehicle pieces and projected fragments can be approximated by circles
of equivalent cross-sectional areas.

c. A person can be represented by a right circular cylinder having a height of h,
feet and a radius of r, feet.

d. A person in the open will be hit by a splatter fragment if two conditions are
satisfied:

April 13, 1995 30


The last bracketed term in Eq. (43) is the effective casualty area for a single projected
piece, given that the piece impacts in the i range interval. If there are N projected
pieces, the conditional casualty area for the i interval can be obtained simply by
multiplying the single-piece area by N, with the proviso that the product does not
exceed some maximum value. This value, termed A,(max), is the maximum possible
area that the projected fragments can endanger while simultaneously moving beyond the
horizontal distance r, and above height h,. For Case (1), A,(max) is the sum of the
shaded areas shown in the plan view of Fig. 14. The sum is easily determined to be

Case (1): A(max) = n (21,4, + 21,4, - 2r,x, - 12) (45)

Figure 14. Limits on Casualty Area for Splatter

Similar diagrams can be drawn and maximum areas computed for the other cases
depicted in Fig. 13, with the following results:

Case (2): A(max) = nd, (21, - d)

Tr, 7 r- 1) (46)
0

Case (3): A,(max)

Case (4): A,(max)

April 13, 1995 39


where r, is the radius of a person, r; is the piece radius, and d is given by Eq. (3).
Previously, the area given by Eq. (4) was called the basic casualty area for the piece.

The effects that impact path angle and fragment size have on casualty area are shown
in Table 1. For these computations r, is 1.0 foot and h, is 6.0 feet. The table entries
show the ratios of the casualty areas computed from Eq. (4) (shown in Fig. 2) to those
from Eq. (2) (shown in Fig. 1) for various path angles.

Table 1. Effect of Impact Path Angle on Casualty Area

Fragment Ratio of Areas
Radius
(ft) y= 90° | y = 88° | y = 85° | y= 80° | y= 70° | y=50°
0.5 1.00 1.09 1.22 1.45 1.93 3.14
1.0 1.00 1.07 1.17 1.34 1.70 2.60
2.0 1.00 1.04 1.11 1.22 1.46 2.07
3.0 1.00 1.03 1.08 1.17 1.35 1.80
4.0 1.00 1.03 1.07 1.13 1.28 1.64
5.0 1.00 1.02 1.06 1.11 1.23 1.53
6.0 1.00 1.02 1.05 1.10 1.20 1.46
8.0 1.00 1.01 1.04 1.07 1.15 1.36
10.0 1.00 1.01 1.03 1.06 1.13 1.29

6. Slide or Skid

After impact, a body that slides or skids along the surface in coming to rest is unlikely
to do so smoothly. More likely, its motion will be some complicated combination of
slide, skid, tumble, roll, and bounce that defies accurate analysis. To estimate the
additional casualty area that such motion produces, the travel distance is calculated as
though the body were in pure slide, thus resulting in constant deceleration. To avoid
underestimation of the distance, conservative slide coefficients must be chosen.

In estimating slide distances, two types of surfaces are considered, namely, a hard
(presumably regular) surface and a soft (perhaps irregular) surface. Except for the
assigned coefficients of friction, the slide calculations are the same for both surfaces. In
estimating the casualty area due to slide for people in the open, the type of surface for
each group of people must be specified. If the type is unknown or not indicated, the
assumption is made that the surface is hard.

6.1 Slide Equations
Given the initial horizontal component of velocity at impact and the coefficient of sliding

friction between a moving and a stationary body in constant contact, the distance the

April 13, 1995 7


and the velocities needed for splatter fragments to reach these ranges are small, vacuum
calculations can be made in evaluating kinetic energies without significant error. The
weighted KE for each interval is calculated as the product of the mean KE needed for
the mean piece to reach the midpoint of the interval and the probability that the piece
impacts in the interval. The range r, to the midpoint of the i interval is given by
Eg. (35), and the probability of impacting in the interval by Eq. (36), where the interval
width w = ty../n. The total average KE imparted to the mean projected fragment can
be written in equation form as follows:

KE(mean projected fragment) = > [Ke (mean)] [Probe 66)
i=l

where KE,(mean) is the mean kinetic energy needed by the mean projected fragment to
reach range 1,.

The total number of projected pieces can now be estimated by dividing the percentage
of KE of the impacting body that is transferred to projected fragments by the KE of the
mean projected fragment determined from Eg. (56). In equation form,

_ _(F)(KE of impacting body) (57)
KE(mean projected fragment)

where N is the number of projected fragments and F* is the fraction of the kinetic
energy of the impacting body that is transferred to the projected pieces. Although
Eq. (57) does not generally produce an integral number of pieces, the use of fractional
pieces in the casualty-expectancy calculations causes no difficulty.

Like many assumptions in this report, assuming that F, for hard surfaces is four times
as large as F, for soft surfaces cannot be fully justified. Intuition certainly suggests that,
for a soft-surface impact, considerably more impact energy will be consumed in
displacing impacted material laterally and throwing it from the resulting crater. If the
coefficient of restitution for a hard-surface impact is about twice that for soft surfaces,
which does not seem unreasonable, a piece rebounding from a hard surface will be four
times as energetic as the same piece rebounding from a soft surface. Intuition further
suggests that the number of splatter fragments produced by a soft-surface impact should
be about the same as, or somewhat less than, the number resulting from a hard-surface
impact. Using a value of F, = 4F, in Eq. (57) seems consistent with this notion.

* The subscripts h and s are used to designate kinetic-energy fractions for hard and
soft surfaces, respectively.

April 13, 1995 49


where W is the explosive yield in pounds of TNT. If, for any B, the velocity required
to reach the midrange of the interval exceeded the velocity given by Baker’s equation,
the value of B was doubled and the velocity recalculated. The doubling was continued
until a suitable velocity was obtained to use in the kinetic-energy calculations.

Table 14. Estimates of Kinetic Energy (ft-lb x 10’) Imparted to
Fragments For the S-IVB-EAFB Accident

Initial Projection Angle (y)

B (lb/ft?) 15° 30° 45° 60°
5 5.2 2.1 49 3.9
10 13 11 17 34
20 0.28 0.18 0.19 0.38
40 0.17 0.10 0.096 0.13
80 0.14 0.086 0.076 0.093

Table 15. Estimates of Kinetic Energy (Ib. of TNT) Imparted to Fragments
For the S-IVB-EAFB Accident

Initial Projection Angle (y)
Bdb/f2) | 15° 30° 45° 60° 75° | Mean
5 34 14 32 25 32 27.4
10 8.3 6.8 11 22 29 15.4
20 18 1.2 1.2 25 18 4.94
40 11 0.68 0.63 0.84 3.0 1.25
80 0.94 0.56 0.49 0.60 13 0.78
Mean 9.95

Since ballistic coefficients and initial path angles of fragments projected from an
explosion vary considerably, the results in Tables 14 and 15 based on quasi-constant
ballistic coefficients and path angles are, at best, rough estimates. Nevertheless, some
KE estimate must be established, so RTI has assumed that the mean of the 25 entries in
Table 15 (or Table 14) produces the best estimate of the total KE acquired by vehicle
fragments. The percent of explosive energy imparted to the projected pieces in the form
of kinetic energy for the S-IVB-EAFB accident is found by dividing the mean of
9.95 pounds of TNT by the TNT yield from Table 12. The results from this and three
other vehicle accidents (not including PYRO-275) are given in Table 16. For the four
accidents, the mean percentage of explosive energy converted into kinetic energy was
computed to be 0.19%.

April 13, 1995 47


9. Composite Casualty Area

Before the total effective casualty area for an inert debris class can be calculated, a
composite casualty area must be determined for the mean piece in the class. The
cross-sectional area of the mean piece augmented by wind and impact-angle effects is
accounted for by using Eq. (4). To this area must be added the casualty area due to one
of the following:

(1) Slide or skid: Eq. (6)

(2) Bounce:
For the i® rebound angle:
Bounce height < h,: Eq. (18)
Long bounce with bounce height > h,: Eq. (22)
Short bounce with bounce height > h,: Eq. (26)
Weighted sum for all rebound angles: Eq. (32)

(3) Splatter: Eqs. (44) and (47)

As defined in this report, the three augmenting effects are mutually exclusive, since an
impacting piece that bounces intact cannot simultaneously break up or slide along the
ground, and since a piece that slides or bounces remains essentially intact while one that
splatters is assumed to break apart.

In earlier RTI studies", the inert pieces produced by destruct breakup of
Atlas IIAS and Delta-GEM vehicles have been separated into debris classes, according
to piece characteristics. To illustrate the results of procedures developed in this report,
casualty areas have been computed for the mean piece in each debris class. Results are
presented in the appendices.

April 13, 1995 53


Table A3. Atlas IAS Effective Casualty Areas for Hard-Surface Impacts

Avasic Agiae Agounce Appt Age Ratio

Class (ft) (ée) (fe) (ft) (fe) Aca! Ava
Al 23.04 16.94 21.63 0 44.67 19
A2 48.22 26.80 36.23 0 84.44 18
A3 26.41 18.98 29.52 0 55.93 2.1
A4 41.84 25.48 47.85 0 89.69 21
AS 19.08 16.13 32.99 0 52.07 2.7°
A6 7.73 9.36 20.78 0 28.51 3.7
A7 49.29 29.00 70.34 0 119.63 24
A8 9.91 12.05 31.39 0.55 41.30 4.2
AQ 8.50 11.04 28.55 0.32 37.05 4A
A110 23.23 19.81 55.39 1.73 78.63 3.4
All 11.45 13.75 37.97 0.64 49.42 43
Al2 100.38 44.54 151.33 24.83 251.70 25
Al3 7.90 11.26 30.65 1.19 38.56 49
Al4 38.19 0 84.13 12.00 132.32 3.2
Al5 9.91 0 36.65 2.80 46.57 4.7
Al6 6.79 0 28.47 3.95 35.26 5.2
Al7 5.03 0 23.64 1.40 28.67 5.7
A18 11.46 0 38.74 4,23 50.20 44
Alg9 60.66 0 89.61 120.73 181.40 3.0
A20 13.32 0 33.72 17.35 47.05 35
A21 24.60 0 36.64 90.04 114.64 4.7
A22 4Al 0 0.03 8.49 12.89 29
A23 6.54 0 0.04 33.78 40.32 6.2
A24 21.95 0 0 426.61 448.56 20.4
Pl 35.54 22.33 30.18 0 65.72 18
P2 34.20 24.35 68.58 3.86 102.78 3.0
P3 57.41 0 109.65 51.26 167.06 29
Pp4 14.24 0 45.74 13.89 59.97 42
P5 52.07 0 0 734.24 786.31 15.1
cl 17.99 15.90 35.33 0 53.32 3.0
C2 14.53 15.08 40.40 0.16 54.93 3.8
C3 21.15 19.18 54.74 3.33 75.89 3.6
C4 6.25 0 26.84 2.88 33.10 5.3
Cc 10.00 0 8.74 20.58 30.57 3.1
C6 * 5.81 0 0 54.78 60.69 10.3
Cc7* 6.45 0 0 94.51 101.05 15.4
C8 * 148.94 0 0 1046.18 1194.93 8.0
co* 148.59 0 0 1521.39 1669.88 11.2
C10 * 148.99 0 0 1001.15 1149.94 7.7
C11 * 148.60 0 0 1507.53 1656.03 11.2

* Data for these classes taken at 20 seconds

April 13, 1995

57



(or assumed) for N before the total effective splatter area can be computed for the
impacting fragment. The only pieces of interest are those projected beyond the
periphery of the impacting component in accordance with the density function, f(r),
shown in Fig. 9. As pointed out previously, no experimental or accident data for
impacting inert pieces could be found to serve as a guide.

In general, most splatter pieces are expected to originate from the impacting body rather
than the impacted surface, since cratering may not occur at all except for fragments with
large ballistic coefficients. If this is the case, the number of splatter pieces should be
related in some way to the mass of the impacting body. Other imponderables add to
the uncertainty of estimating the number of splatter fragments produced. For example,
a module consisting of many individual components will likely produce more splatter
fragments than a more homogenous body with the same weight and KE/A, although
even this depends on the frangibility of the impacting body.

To make progress, some assumptions must be made about the average number of
projected pieces produced by an inert impact, even though the assumptions are
conjectural in nature. Although no empirical data could be found for inert impacts,
limited data from five accidental space-vehicle explosions were discovered in CPIA
Publication 394". For these relatively large explosions where the TNT equivalency
was estimated to be 1000 pounds or more, the number of recovered pieces varied from
40 to 949, For the two smallest explosions, both with estimated yields of 1000 pounds,
44 and 60 projected pieces were recovered. It seems likely that other pieces were not
found or were considered too small to be of interest even though small high-speed
projectiles may be hazardous to people in the open. Fragment data from the five
accidents are given in Table 12.

Table 12. Fragment Data from Vehicle Accidents

Total Fragment | TNT Yield | No. of Pieces
Test Vehicle (accident date) Weight (1b) (Ib) Recovered
Atlas Centaur (3-2-65) 9085 1930 40
S-IVB-ASTV (1-24-64) 1882 1000 44
S-IV-EAFB (7-14-65) 3125 3200 412
S-IVB-503 (1-20-67) 1426 2300 949
PYRO-275 (3-22-67) 1628 1000 60

For the five vehicle accidents, the CPIA Publication (Fig. 2-35) provides graphs of total
fragment weight in percent versus fragment range from the explosion in feet. Since the
plot for PYRO-275 was incomplete, it was discarded. In other cases, graphs were either

April 13, 1995 45


in Sections 7.2, 7.3, and 7.4, RTI has assumed that the hard-surface and soft-surface
coefficients of restitution for low-impact-velocity debris are 0.5 and 0.25, respectively.

7.5 Assumed Coefficient of Restitution and Bounce Results

Since the coefficient of restitution e depends — among other things — on impact
velocity after some minimum velocity is exceeded, the assumption has been made
that e varies inversely with the logarithm of impact velocity Vp beyond this minimum
value. The assumed relationships are shown in Fig. 4, one for impacts on hard surfaces,
the other for impacts on soft surfaces. For hard surfaces, e has a constant value of 0.50
for Vip less than or equal to 40 feet per second, and thereafter decreases linearly (in the
log domain) to zero for Vp = 300 feet per second. In equation form,

e = 0.50 (Vp, < 40)

(16)
e = 1415 - 0.5714log,(V_) 40 < Vp < 300)

For soft surfaces, e has a constant value of 0.25 for Vip less than 60 feet per second, and
thereafter decreases to zero for Vp = 200 feet per second. In equation form,

0.25 (V,, < 60)

1.100 - 0.4781 1og,,(V,) (60 < Vip < 200)

° a7)

e

April 13, 1995 17


edge of impacting fragment

Figure 12. Fragment Projected Above Height of a Person

As shown in the figure, the fragment is below h, feet and thus hazardous during the
first and last d, feet of horizontal travel rather than for the entire distance r,. (Note: for
vacuum calculations, the two distances labeled d; are equal.) Thus, Eq. (37) must be
revised to reflect this fact. If the projection angle y is known, the projection velocity v,
needed to reach range r, can be calculated by

v= gy (38)
° sin (2y)

where g is the gravitational acceleration (32.174 ft/sec’). The time to reach height h, can
be computed from the equation

_ v,siny - yo, siny) - 2gh, (39)

: g

The distance d; is then calculated by

d, = t, v, cosy (40)

April 13, 1995 35


Table of Contents

April 13, 1995 ii

«Introduction 6.6... ee ec eee ete nnn eee e nee 1
. Casualty Expectancy 1.6... cece cee eee eee e eee eee eens 1
2.1 The Casualty Expectancy Concept . 1

2.2 Identification of Hazardous Pieces ....... 2

. Casualty-Area Computations ©... 6.6... e eee eee ee eee eee 3
. Dimensions of a Person .........6. 00s eee eee Me eee eee tees 4
. Wind and Path Angle Effects... 0.6... c cece cece nee e eee 5
. Slide or Skid 6. eet n tte tenet eens 7
6.1 Slide Equations ...........-.00005 7

6.2 Slide Coefficients and Distances .... 8

6.3 Assumptions ............-505. 2 9

6.4 Casualty Area for Slide or Skid «6... 6... e cece ete eee eee eee 11

. Bounce or Ricochet 2... 0... cece cece eet eee eens 12
7.1 Bounce Equations ....... 2... see ee eee eee eee eee eee 12

7.2 Horizontal Bounce Distance 13

7.3 Height of Bounce .... 6... e cece cece eee 14

7A Estimates of Low-Velocity Coefficients of Restitution 15

7.5 Assumed Coefficient of Restitution and Bounce Results 17

7.6 Casualty Area for Low Bounce .........0 eee e eens 20

7.7 Casualty Area for High Bounce .....--.----+++ +000 20

7.7.1 High and Long Bounce ..........0 eee eens 20

7.7.2 High and Short Bounce ........-. 6-0 eee eee 22

7.8 Multiple Bounces ...... 660s cece cece eee tees .. 24

7.9 Unequal Impact and Rebound Angles ...........0 2000 eee eee eee 25

7.9.1 Density Function for Rebound Angle ........-.-..-+-+55- 25

7.9.2 Computation of Casualty Area for Variable Rebound Angle ... 28

7.9.3 Casualty-Area Example... 0.06.00 05 eee eee eee eee 28

8. Splattering and Cratering 30
8.1 Basic Assumptions . 30

8.2 Splatter-Range Density Function 31

8.3 Casualty Area for Fixed Splatter Range With No Overflight ......... 32

8.4 Casualty Area for All Range Intervals With No Overflight .. -- 33

8.5 Elimination of No-Overflight Restriction ............-- 34

8.6 Maximum Splatter Range .......--.. 6 e eee eee eee -.. 40

8.7 Number and Weight of Splatter Fragments ..........-. 00s eee eee 44

8.8 Frangibility Factor «6.6... eee ee eee eee eee ee eee 50

8.9 Size of Splatter Fragment .... 6.0... 0. eee e eee eee eee -- 50

8.10 Attempt to Obtain Experimental Data .....---- +e eee sree ee eee 52


7.9.2 Computation of Casualty Area for Variable Rebound Angle

So that all values of rebound angle @ between 1/2 and zero are considered in calculating
the casualty area due to bounce, the range of values for is divided into n equal
intervals, with the midpoint of each interval calculated from

$= ear - 1} iL (30)
‘ n 2

For an assumed value of , the horizontal and vertical components of rebound velocity
are first computed, then the distance and height of bounce. If the bounce height is less
than h,, A.(bounce); is determined from Eq. (18). If the bounce height is greater than h,,
a test is made using Eq. (19) to determine whether the bounce is "high and long" or
“high and short". For the first case, A(bounce), is found from Eg. (22); for the latter,
from Eq. (26).

The value of A,(bounce), must now be weighted by the probability that the rebound
angle lies in the interval with midpoint 9, Since the density-function segments are
linear, this probability p, can be found by multiplying the height of the function at @, by
the interval width. Thus

P= fo) — (31)

The same procedure is followed for each assumed value for $,. The casualty area for
bounce is then obtained from

A (bounce) = > p, A (bounce), i = 1,2,,n (32)
isl

7.9.3 Casualty-Area Example

The procedures set forth in Section 7.9.2 for variable rebound angles were applied with
n = 9 for a piece impacting at an angle of 80° (relative to the horizontal) and a speed of
94.3 ft/sec. The resulting casualty-area computations are summarized in Table 9. The
final result of 35.9 ft? for A.(bounce) is significantly greater than the value (15.6 ft’)
obtained when assuming equal incident and rebound angles of 80°.

April 13, 1995 28


V, (ft/sec) = (22)

es]

where p, is the atmospheric density at sea level in slugs/ft* (22.85 x 10* for the US
Standard Atmosphere 1962), and (w/C,A) is the ballistic coefficient B in Ibs/ft?.

Table 4. Bounce Distances

Horizontal Bounce Distance (ft)*
B Vy
(Ibs/ft?) | (ft/sec) | e = 0.05 | e=0.1 | e=02 | e=03 | e=04 | e=06
0.2 13.2 0.02 0.09 04 0.9 15 34
05 20.9 0.04 0.15 0.6 13
1.0 29.6 0.05 0.21 08 19
2.0 41.8 0.07 0.30 12 27
5.0 66.2 0.12 0.47 19 43
10.0 93.6 0.17 0.67 27 6.0
20 132.3 0.24 0.95 3.8 85
50 209.2 0.37 150 6.0 13.5
100 295.8 0.53 2.12 8.5 19.0

* Based on vertical terminal velocity and a horizontal velocity component of 11.5 ft/sec

7.3 Height of Bounce

Since no experimental or theoretical data could be found in establishing values for e, a
selection based on engineering judgement and intuition was necessary. To provide
further insight, height of bounce was calculated from the equation

Pas

h, = ¥ (13)

N)
a

using the same ballistic coefficients and terminal velocities given in Table 4. The results
are: shown in Table 5 for six constant values of e.

April 13, 1995 14


7.6 Casualty Area for Low Bounce

If the vertical component of rebound velocity is less than (2gh,)'/? where h, is the height
of a person, the bouncing fragment will not rise above h,. In this case, the additional
casualty area for bounce is

A, (bounce) = 2(r, + rd, ‘ (18)

where 1; is the equivalent radius of the impacting fragment, r, is the radius of a person,
and d, is computed from Eg. (11). It can be seen that Eq. (18) is the same as Eq. (6)

except d, has replaced d,.
7.7 Casualty Area for High Bounce

For most fragments except possibly early in flight, the path angle of the velocity vector
at impact (relative to the horizontal) is well above 70°. As a result, the height of bounce
can be considerably greater than the horizontal bounce distance. During the period that
the bouncing piece is above height h,, the vulnerable individual may be justifiably
excited although not actually hit. The casualty area computed from Eq. (18) must be
modified to account for this.

7.7.1 High and Long Bounce

Consider first the case depicted in Fig. 5, where the bounce distance is so large that the
position of the piece at height h, on the way up does not overlap the position of the
piece at height h, on the way down. From left to right, four positions of the bouncing
fragment are shown in plan view where, in all cases, the fragment radius 1, has been
augmented by the radius of a person r,:

(1) Position at first impact

(2) Position during first upward bounce when fragment has risen to height h,
(3) Position during first bounce when fragment has descended to height h,
(4) Position of fragment at second impact.

As evident from the figure, a circularized flat piece has been postulated with the flat
surface parallel to the ground throughout the bounce.

April 13, 1995 20


h (14)
e= |=
H

where h and H are the rebound and drop heights, respectively.

For other dropped objects, a different procedure was used to estimate e, since bounce
height and rebound angle were critically dependent on impact attitude. For each of
several drops, the height and distance of bounce were measured (within an inch or so),.
and the rebound velocity needed to produce a trajectory with this apogee and distance
was calculated. The impact velocity for a 9-foot drop was then determined, and e
calculated from the equation

_ V (rebound) (15)
v (impact)

The resulting experimental values for e are given in Table 6. The wide variations in
results for the irregularly-shaped objects show that e is sensitive to impact attitude.

Table 6. Experimental Values for Coefficient of Restitution

Coef. of Restitution
Dimensions Weight Hard Soft
Ttem (inches) (oz) Surface Surface
basketball 9" diameter 20 0.66 0.61
softball 3.5" diameter 64 0.60 0.08
tennis ball 2.5" diameter 2.0 0.72 0.52
wood block 1.5" x 1.5" x 3.2" 15 0.21-0.50 | 0.24 - 0.33
steel bolt and nut 4.2" long, 0.25" diam. 1.7 0.30 - 0.43 | 0.00 - 0.20
thin steel cup 1" deep x 2.75" diam. 18 0.26 - 0.48 | 0.15 - 0.24

At best, the results in Table 6 serve only as a rough guide in estimating coefficients of
restitution for low-velocity impacts of space-vehicle debris. It seems apparent that the
hard-surface values should be chosen well below those computed for the three balls, yet
somewhat higher than the experimental values obtained for other items, since some
space-vehicle debris could well be more resilient. If any proof is needed, the drop tests
also show that the hard-surface coefficients are generally well above those for soft
surfaces, with maximum values about twice those measured for soft surfaces. Since
values chosen for e will be applied to widely diverse components and debris, agonizing
over the values to be selected is not justified. Accordingly, based on the data presented

April 13, 1995 16


Table 9. Bounce Casualty Area Using Variable Rebound Angles

Interval Bounce | Casualty Weighted
i o; height distance | A,(bounce), PB Abounce),
(deg) (ft) (ft) (ft) (ft)

1 5 0.1 3.9 12.3 0.015 0.186

2 15 0.8 11.4 35.5 0.040 1.414

3 25 2.0 17.4 54.5 0.064 3.511

4 35 3.7 214 66.8 0.089 5.957

5 45 5.7 22.7 71.1 0.114 8.094.

6 55 7.6 14.0 43.7 0.139 6.048

7 65 9.3 9.5 29.6 0.163 4,832

8 75 10.6 6.3 19.8 0.188 3.724

9 85 11.3 3.7 11.1 0.188 2.091

Total - - - - 1.000 35.858

The nine intervals shown in Table 9 were used to illustrate the procedure for variable
rebound angle. When using 45 intervals, the final result for A(bounce) is 35.4 ft.

April 13, 1995 29


6.4 Casualty Area for Slide or Skid

The computation of casualty area due to slide is illustrated in Fig. 3, where the sliding
fragment of radius r, has been augmented by the radius of a person r,, and d, is the slide
distance computed from Egs. (5).

°
direction position
of slide after slide

Figure 3. Casualty Area Due to Slide

The additional casualty area due to slide is

A, (slide) = 2(, + 1,)d, (6)

In evaluating A,(slide), the area (n/2)(r; + r,)* is both added and subtracted from the
right-hand member of Eq. (6). It is added to account for the semi-circular area occupied
by the leading half of the augmented fragment at its position after slide; the same area
must also be subtracted to avoid counting it twice, since the area occupied by the
leading half of the augmented fragment at impact has already been accounted for in the
basic casualty area given by Eq. (4).

Although Fig. 3 depicts the case where d, > r; + rp, exactly the same result is obtained
if d, Sry +r).

April 13, 1995 11


Table A1. Atlas ITAS Debris Characteristics

Weight | Cross-sect. | Subsonic | Terminal Vel.
Class | Description (Ib) Area (ft?) | B (lb/ft?) (ft/sec)
Tank frags 2.99 3.53 0.98 29.3
Tank frags 14.75 16.04 1.05 30.3
Tank frags 6.16 5.38 1.24 32.9
Tank frags 18.22 13.85 1.54 36.7
Tank frags 431 2.91 1.72 38.8
Prestart solenoid 0.15 0.06 2.10 42.9
Miscel. frags 46.57 20.08 2.61 478
Miscel. frags 4.95 0.68 4.66 63.9
Miscel. frags 1.80 0.37 4.89 65.4
Miscel. frags 31.70 6.24 5.06 66.5
LO2 inlet elbow 11.00 1.42 8.60 86.8
Large payload fairing | 1908. 61.33 9.63 91.8
Major frags 5.00 0.43 10.16 94.3
Major frags 216. 16.35 12.30 103.8
Major frags 13.51 1.15 16.89 121.6
Miscel. frags 8.49 0.34 25.06 148.1
Miscel. frags 1.43 0.05 25.34 148.9
Miscel. frags 39.75 1.88 27.55 155.3
Major frags 1236.8 33.64 36.04 177.6
Major frags 65.47 2.83 43.06 194.1
Major frags 315.67 9.03 50.33 209.9
Miscel. frags 4.10 0.04 100.00 295.9
Miscel. frags 43.26 0.43 100.00 295.9
Booster turbo pump 1056. 7.94 190.00 407.8
Spacecraft frags 25.20 9.25 1.05 30.3
Spacecraft frags 123.27 12.10 435 61.7
Payload module 1115.8 29.90 14.60 113.0
Spacecraft frags 85.71 2.80 14.74 113.6
Bus module 5372.8 28.60 187.9 405.5
Castor frags 5.36 2.74 2.09 42.8
Castor frags 9.17 2.19 4.69 64.1
Nozzle closure 40.00 5.58 7.20 79A
Castor frags 4.22 0.24 27.50 155.1
ADJ thruster arm 65.00 1.53 70.80 248.9
Castor prop. frags 18.00 0.30 133. 341.2
Castor prop. frags 35.00 0.47 165. 380.0
GL Castor (dest.) 14387. 107.5 555. 697.0
AL Castor (dest.) 21936. 107.5 847. 861.0
GL Castor (ISDS) 13711. 107.5 529. 680.5
AL Castor (ISDS) 21713. 107.5 838. 856.4

* Weights for these classes taken at impact following failure at 20 seconds

April 13, 1995

55



3. Casualty-Area Computations

The casualty area associated with an impacting piece or component is a theoretical
region on the ground within which 100 percent casualties occur and outside of which
no one is injured. In reality, no such physical area exists. Rather the effective casualty
area, as developed in this study, is a numerical quantity which, on the average, gives the
proper answer in the casualty-expectancy equation. (The terms ‘effective casualty area’
and ‘casualty area’ will be used interchangeably.)

For people in the open, the effective casualty area for an impacting inert piece may be
considerably larger than the maximum cross-sectional area of the piece itself to account
for the following:

dimensions of a person,

. wind and trajectory path angle,
slide or skid,

. bounce or ricochet,

splattering and cratering.

eno gD

For every falling piece, the dimensions of a person (item a) and the effect of trajectory
path angle at impact (item b) must be included in the casualty-area evaluation. As
shown later, both items are accounted for in a single equation to produce a basic
casualty area for the piece. The three supplemental effects of slide, bounce, and splatter
are considered to be mutually exclusive. One of the three is assumed to occur even
though in unusual cases an impacting piece may bury itself without ejecting debris
beyond the rim of the impact area. The casualty areas associated with all three
supplemental effects are evaluated, and a composite casualty area obtained by adding
the largest of the three to the basic casualty area. For application in RTI's risk
computation program, facility DAMage and Personnel injury (DAMP), the composite
casualty areas for inert debris for people in the open are computed off-line for each class
of debris. The areas are input to DAMP as a function of time from launch.

The five effects (a through e above) that must be accounted for in evaluating the
effective casualty area for an inert piece for a person in the open are discussed
individually in the sections that follow.

For people in buildings or shelters, the casualty area of a piece may be larger or smaller
than its maximum cross-sectional area, depending on the capability of the piece to
penetrate or perforate the structure. If the piece is incapable of penetrating or causing
internal structural damage, the effective casualty area for the piece is zero for that
structure. Thus for a sheltered person, the effective casualty area associated with a
falling inert piece must account for:

a. capability of piece to penetrate or perforate the structure,

April 13, 1995 3


O,G \eeeennneee ence cece cece cece ccna cee eccnnennegpeneee
{( for G= 0°

{(M for g= 90°

0 Ne

Rebound Angle @

Figure 7. Rebound-Angle Density Function for
Impact Angles of 90° and 0°

Since the area under the curve must be unity, the constant C = 4/n, and the
density-function equations for rebound angle » become

Impact angle o, = 90°: fl¢) = =o

(27)

- 56

Impact angle , = 0°: f(g) = =

ale Alo

The further assumption is made that the rebound velocity can be calculated from
Eq. (15) for any rebound angle, i.e., v(rebound) = e v(impact).

The density-function curves in Fig. 7 for impact angles of 90° and 0° served as a basis
for postulating the density-function curve shown in Fig. 8 for any intermediate impact
angle , It can be seen that the most likely rebound angle is equal to the impact angle,
while the changes in probability for rebound angles greater than and less than the
impact angle are at the same constant rates assumed for the impact density functions for
0° and 90°.

April 13, 1995 26


Table B3. Delta-GEM Effective Casualty Areas for Hard-Surface Impacts

GP2 *
GP9 *
Gcl
GC2

* Data for these classes taken at 20 seconds

Revised November 10, 1995

7.38
7.17
7.13
29.54
191.05
189.63
5.58
442
9.73
12.49
28.20

oooocococococecoceocooc]oe

13.71
21.86

9.83

9.68

5.88
19.50

0

0

0
17.93

0
36.18
60.77

62

14.21
53.56
64.62
349.67
1039.92
36.47
2.27
179.47



10.
11.

12.
13.
14.

15.

References

Montgomery, Robert M, and Ward, James A., "Facility Damage and Personnel Injury
From Explosive Blast", April 16, 1993, RTI/5180/26-08F, Research Triangle Institute,
prepared for Directorate of Safety, 45 SPW/SE, Patrick AFB, FL, and 30 SPW/SE,
Vandenberg AFB, CA.

AF Regulation 127-100, Explosive Safety Standards, Glossary, page 142,20 May 1983.

Haber, Jerold M., and Heubach, William F., "Estimation of Casualties From.
Impacting Debris", ACTA Inc., Technical Report No. 89-217/15-01, September 29,
1989, prepared for Department of Air Force.

Handbook of Chemistry and Physics, Chemical Rubber and Publishing Company.

Clements, Guy R., and Wilson, Levi T., Analytical and Applied Mechanics, McGraw-Hill
Book Company Inc., page 237.

Shames, Irving H., Engineering Mechanics: Dynamics, Prentice-Hall Inc., 1960,
page 454.

Document 361-83, Meteorological Group, Range Commanders Council, "Cape
Canaveral Florida: Range Reference Atmosphere", February 1983, page 65.

Montgomery, R. M., and Ward, J. A., "Computations of Hit Probabilities From
Launch-Vehicle Debris", RT1/4666/02F, September 19, 1990.

Ahlers, Edward B., "Fragment Hazard Study", Minutes of Eleventh Explosive Safety
Seminar, Vol. I, Armed Services Explosive Safety Board, Washington, DC,
9-10 September 1969.

Kornhouser, M., Structural Effects of Impact, Spartan Books Inc., Baltimore, MD.

Henny, R. W., and Carlson, R. H., “Distribution of Natural Missiles Resulting From
Cratering Explosions on Hard Rock", Prevention and Protection Against Accidental
Explosions of Munitions, Fuels and Other Hazardous Mixtures, Annals of the NY
Academy of Science, 152, Art. 1, 1968.

Ahlers, Edward B., "Debris Hazards, A Fundamental Study", DASA-1362, 1963.
Montgomery, R. M., unpublished working paper, “Casualty Expectancy", 1987.

Chemical Propulsion Information Agency Publication 394, Vol 1, 13 Nov 1985,
Table 2-11 on page 2-21, and Figs. 2-34 and 2-35 on pages 2-80 and 2-81.

Baker, Wilfred E., et al., "Workbook for Predicting Pressure Wave and Fragment
Effects of Exploding Propellant Tanks and Gas Storage Vessels", NASA CR-134906,
September 1977.

April 13, 1995 64


16. Refling, O., Stern, R., Potz, C., "Review of Orbital Reentry Risk Predictions", The
Aerospace Corporation, ATR-92(2835)-1, 15 July 1992.

17. Letter of transmittal from National Transportation Safety Board to RTI, January 26,
1995, by Robert Benzon, Sr. Air Safety Investigator.

18. Ward, J. A., and Montgomery, R. M., "Atlas IAS Debris Model for HITP",
RTI/5180/26-13F, September 30, 1993.

19. Ward, J. A., and Montgomery, R. M., "Delta-GEM Debris Model for HITP",
RTI/5180/02F, September 30, 1992.

20. Ward, J. A., and Montgomery, R. M., "GEM Breakup Data With Case-Splitter
Destruct Package", RTI/5180/26-11F, September 30, 1993.

April 13, 1995 65


,-2d - G+pl

Position at i : : i Position at
first impact i second impact

Figure 6. Plan View for Short-Bounce Fragment

In summing the component areas that comprise A,(bounce), the area A formed by the
intersection of the two solid-line circles must not be included twice. It can be found by
multiplying the shaded area shown in the figure by four. If the origin of the orthogonal
X-Y coordinate system is chosen at O with the X-axis along the centerline of the
bouncing piece, the equation of the left-hand circle is x* + y’ = 1°. Then

A =4{(t? - x)? dx (24)

pees

where a = (d, — 2d)/2 and r = (r, + r,). Performing the integration and simplifying,

A = mr? - 2ayr? - a? - 2a [2] (25)

r

After evaluating A, the casualty area can be found for the high and short bounce, where
d, < 2d +1;+1,). In summing the component areas shown in Fig. 6 to arrive at an

April 13, 1995 23


Table of Tables.

Table 1. Effect of Impact Path Angle on Casualty Area 7
Table 2. Coefficients of Sliding Friction -. 8
Table 3. Horizontal Slide Distance ..... 9
Table 4. Bounce Distances ...... 14
Table 5. Bounce Heights ........ ee eee ee sence eee e eee vee
Table 6. Experimental Values for Coefficient of Restitution .... «+. 16
Table 7. Bounce Distances and Heights ..........--0eee eee e eens s+. 19
Table 8. Multiple Bounce Heights and Distances on Hard Surfaces ...... o1. 24
Table 9. Bounce Casualty Area Using Variable Rebound Angles see -1. 29
Table 10, Component Characteristics .....--. 0. eee eee tenes ... B
Table 11. Maximum Splatter Range (tyax) ++ se we. 4€
Table 12. Fragment Data from Vehicle Accidents .......... 00sec eee eee eee 45
Table 13. Percent of Total Weight of Fragments Within Indicated Range ........ 46
Table 14. Estimates of Kinetic Energy (ft-lb x 10’) Imparted to Fragments For

the S-IVB-EAFB Accident ...... 6. cee eee cece eee eee eee eens 47
Table 15. Estimates of Kinetic Energy (lb. of TNT) Imparted to Fragments For

the S-IVB-EAFB Accident ....... 6. cece cece eee e nett erences 47
Table 16. Percent of Explosive Energy Converted into Fragment Kinetic Energy .. 48
Table 17. Sample Projected Fragment Sizes ... 2.0... cece eee ete teens 51
Table 18. Sample Splatter Parameters for Hard-Surface Impacts .. wee 51
Table A1. Atlas IIAS Debris Characteristics .........0-- eee eee . 55
Table A2. Atlas IIAS Splatter Parameters ..... 50.06. c eee eee eee - 56
Table A3. Atlas ILAS Effective Casualty Areas for Hard-Surface Impacts - 57
Table A4. Atlas IIAS Effective Casualty Areas for Soft-Surface Impacts . 58

Table B1. Delta-GEM Debris Characteristics
Table B2. Delta-GEM Splatter Parameters ........ 0066 cess eee eee eee eens

Table B3. Delta-GEM Effective Casualty Areas for Hard-Surface Impacts ....... 62
Table B4, Delta-GEM Effective Casualty Areas for Soft-Surface Impacts ........ 63

April 13, 1995 iv


9. Composite Casualty Area 1... eee ccc eee etna 53

Appendix A. Effective Casualty Areas for Atlas IIAS Debris ...............- 54
Appendix B. Effective Casualty Areas for Delta Debris .... vee eeetueeeeees 59
References 2.6... c eee eee e teen eee eeee 64

Table of Figures

Figure 1. Casualty Area for Piece Falling Vertically .............

Figure 2. Casualty Area for Piece Falling Diagonally

Figure 3. Casualty Area Due to Slide...............4.- see
Figure 4. Coefficients of Restitution for Bounce ......... ese e eee e eee ee ees
Figure 5. Plan View for Long-Bounce Fragment ..........0 20sec eee ee eeeee
Figure 6. Plan View for Short-Bounce Fragment ..........000eeeeseeee .
Figure 7. Rebound-Angle Density Function for Impact Angles of 90° and 0° . 26
Figure 8. Rebound-Angle Density Function for Intermediate Impact Angle ...... 27
Figure 9. Splatter-Range Density Function ........ 000. ee eee eee eee eeee se. 31
Figure 10. Casualty Area for Splatter Fragment ...........0 0002 eeee +e. 32
Figure 11. Splatter-Range Density-Function Interval ...............4. +e. 33
Figure 12. Fragment Projected Above Height of a Person ............ . 35
Figure 13. Fragment Trajectory Geometry .....-. ss eee eeeeeee eee -- 38
Figure 14. Limits on Casualty Area for Splatter ........... 0000 cece seen eens 39

April 13, 1995 iii


7. Bounce or Ricochet

Since falling pieces have both vertical and horizontal components of velocity, bodies that
remain essentially intact after impact may bounce or ricochet along the impacted surface,
thereby increasing their effective casualty areas. If a body breaks up and disperses upon
impact, it is not considered as a bouncing body even though some dispersing fragments
do in fact bounce. Instead, the dispersing or bouncing fragments are treated as splatter
fragments, and the additional casualty area due to splattering is calculated as discussed
ina later section (Section 8) of this report. For pieces with small ballistic coefficients and
thus low impact velocities, bounce and slide are, probably indistinguishable from
ricochet. Except for the effects of wind, such pieces would impact nearly vertically.
Even pieces with large ballistic coefficients are likely to impact at high path angles with
respect to the horizontal, except possibly early in flight when vehicle breakup may result
in relatively high horizontal velocities at impact. For steep path angles, ricochet is
unlikely to occur but, if it should, would appear as an integral part of splattering,
bounce, or slide. For these reasons, the casualty area due to possible ricochet was
assumed to be a part of one of these effects.

It is certainly possible for an impacting piece to bounce more than once. Because of the
uncertainty in the overall process, bouncing pieces are considered to be hazardous
during the first bounce only.

In estimating casualty area due to bounce, both hard and soft surfaces are considered.
Except for the functions used to define the coefficients of restitution, the procedures and
equations for the two surfaces are identical. In making risk calculations for people in
the open, the type of surface on which each person or group of people is located must
be specified. If the type is unknown or not indicated, the assumption is made that the
surface is hard.

7.1 Bounce Equations

A rough estimate of bounce distance can be made by estimating the rebound velocity
after impact. In general, the rebound velocity for a body may be calculated as

v(rebound) = e Jv? + v? ”

where e is the coefficient of restitution, and v, and v, are the vertical and horizontal
components of velocity at impact. If the angles of impact and rebound are equal, then

(rebound) = tanTM | (8)

Vn

April 13, 1995 12


injury to people and that, on the average, five people are injured in each accident. Then,
the probability of casualty is 1/1000, whereas the casualty expectancy is 5/1000 or 1/200.
In unusual situations, casualty expectancy may be greater than one, while the probability
of casualty can never be.

2.2 Identification of Hazardous Pieces

An individual is considered a casualty if he is directly hit by a primary falling piece, or
by a sufficiently energetic bouncing, ricocheting, or skidding piece, or by secondary
crater ejecta or piece fragments projected outward from an impacting piece at velocities
above some threshold value. In other words, if a person is physically occupying space:
which a moving fragment would otherwise pass through or impact upon, he or she is
a casualty by this definition. This definition is not consistent with the one that has
appeared in Air Force explosive safety standards”, where a hazardous piece has been
defined as one possessing 58 ft-lb of kinetic energy at impact. Presumably, this is the
threshold for serious rather than minor injury, since a one-pound piece must fall at least
58 feet, or a 58-pound piece one foot, to acquire this kinetic energy. To put it another
way, a one-pound piece must attain a speed of 61 ft/sec, a two-pound piece 43 ft/sec,
and a 58-pound piece 8 ft/sec to have kinetic energies of 58 ft-lb. Such energetic pieces
might well be permanently disabling or lethal.

If any person who is hit is regarded as a casualty, the seeming effect is to consider all
falling pieces as hazardous, i.e., to set the kinetic-energy threshold at zero foot-pounds.
In application, this is not generally done, since light pieces with small ballistic
coefficients may not be included in the vehicle breakup data, or they may be eliminated
from the risk calculations by the safety analyst. The difficulty in establishing a suitable
threshold is pointed out on page 1-10 of an ACTA report®!, where a tackled football
player who experiences an energetic impact of 400-500 foot-pounds is typically
uninjured, while an individual stopping a 38-caliber bullet having a kinetic energy of
only 120 foot-pounds may well be killed. As another example of why kinetic energy
alone is not a good indicator of hazard, a vehicle skin piece having an area of one square
foot and a tumbling ballistic coefficient of two has a vertical velocity component at
impact of about 21 ft/sec and a kinetic energy of about 8 ft-lbs. A broad-side impact
from such a piece may leave a person unscathed, while a slashing end-on impact may
result in a serious wound.

In view of the foregoing difficulties in establishing suitable kinetic-energy thresholds,
RTI regards all pieces included in the hit-probability and casualty-expectancy
calculations as hazardous to people in the open. It is left to the analyst to avoid ultra
conservatism by eliminating from the calculations any pieces that present negligible
risks.

April 13, 1995 2


—_— hard surface
-— - soft surfact

Coefficient of Restitution, e

0.0 2 : i :
10 30 100 300

Impact Velocity (ft/sec)

Figure 4. Coefficients of Restitution for Bounce

Although no real justification can be provided, the basis for the assumed relationships
in Fig. 4 is as follows:

(a)

(b)

(c)

April 13, 1995

They are consistent with the notion that, beyond some relatively small impact
velocity, e should decrease with velocity, since the energy consumed in
deforming both the impacting and impacted bodies increases with velocity.
For high values of e, relatively little energy is lost in deforming either body.

For impacts on hard surfaces at small impact velocities (<40 ft/sec), e has a
value of 0.50, which is well below the values obtained experimentally for three
types of balls, and below the value given in Ref. [5] for iron impacting on iron.
(Available handbooks do not provide coefficients for impacts of metallic
objects on concrete, rock, or sand.) Smaller values of e are assigned for soft
surfaces, since surely the bounce on soft surfaces would be less.

For space-vehicle debris, it seems apparent that e will never decrease with
velocity in a predictable or consistent manner. Since a linear decrease leads
to unreasonable bounce heights for high impact velocities, some more rapidly
decreasing function is needed. Logarithmic functions produce (seemingly)

18


RESEARCH TRIANGLE INSTITUTE ZRII

Contract No. FO4703-91-C-0112
RTI Report No. RTI/5180/60-31F
April 13, 1995

Casualty Areas from Impacting Inert Debris
for People in the Open

Final Report

Prepared for

Department of the Air Force
45th Space Wing (AFSPC)
Directorate of Safety - 45 SW/SE
Patrick AFB, FL 32925

and

Department of the Air Force
30th Space Wing (AFSPC)
Directorate of Safety - 30 SW/SE
Vandenberg AFB, CA 93437

Distribution authorized to US Government agencies and their contractors to protect administrative/
operational use data, 13 April 95. Other requests for this document shall be referred to the 30th Space
Wing (AFSPC) Directorate of Safety (0 SW/SE), Vandenberg AFB, CA 93437, or 45th Space Wing
(AFSPC) Directorate of Safety (45 SW/SE), Patrick AFB, FL 32925.

3000 N. Atlantic Avenue + Cocoa Beach, Florida 32931-5029 USA

&&
Qe


In making operational plans based on damage predictions, it must be borne in
mind that the confidence level of prediction is inherently low. Even in
well-controlled laboratory determination of damage, wide scatter is commonly
obtained in the data for supposedly identical specimens tested under repeatable
conditions. - - + It is because of the inherent nonreproducibility of practical
impact situations that the approximate and quick prediction methods presented
here are valuable. More ‘accurate’ calculations will usually provide only the
illusion of accuracy:

In view of this, it seems apparent that only "ball-park" approximations can be developed
for highly diverse and deformable components that impact at various velocities in
unpredictable attitudes on uncertain terrain. Since no pertinent experimental data are
available, these difficulties must be tossed aside if progress is to be made.

Kinetic energy (KE) is computed from a component's weight W and impact speed v
using the equation

KE = imy?-l Wy (48)

where g is the mass to weight conversion factor. For use with program DAMP, the
component's impact speed is computed by numerically integrating the equations of
motion to impact, although the speed may also be approximated from the
terminal-velocity equation [Eq. (12)]. Although a relationship between kinetic energy
and splatter range could have been assumed, RTI's visceral feeling is that KE per unit
area is a better parameter for correlation. Some confidence is gained for the assumption
by noting penetration equations presented in Section 3.1 of Ref. [10], although depth of
penetration and maximum splatter range are not necessarily functions of the same
parameters. Using experimental test data, Kornhouser found that depth of penetration Y
could be represented by the expression Y = CWv’/D’, where C is a proportionality
constant and W, v, and D are the impacting projectile’s weight, striking speed, and
diameter. It can be noted that the numerator of the expression for Y is proportional to
kinetic energy and the denominator is proportional to area. As a numerical example
further suggesting that KE/A is a reasonable correlation parameter, consider a
1000-pound piece impacting at 200 ft/sec that has the same KE as a 16,000-pound piece
that floats down on a parachute at 50 ft/sec. Other things being equal, common sense
suggests that breakup and splattering from the 1000-pound piece should be more
extensive. In all likelihood, the cross-sectional area of the 16,000-pound piece would be
considerably greater than the corresponding area of the 1000-pound piece, resulting in
a smaller KE/A for the heavier piece.

According to Chemical Propulsion and Information Agency (CPIA) Publication 394,
page 2-47, Henny and Carlson" found that the maximum range of crater ejecta from

April 13, 1995 41


Figure 1. Casualty Area for Piece Falling Vertically

In either case, the casualty area for the piece due solely to the dimensional effects of a
person and the cross-sectional area of the piece becomes

A.(vertical) = n(cr, + 1) 2)

where 1; is the circularized radius of the piece and r, is the radius of a person.
5. Wind and Path Angle Effects

In general, vehicle pieces do not fall vertically as postulated in Section 4. Rather, the
velocity vector v at impact makes some angle y with respect to the horizontal, since
(1) not even the no-wind trajectory is vertical at impact although it may be nearly so for
pieces with low ballistic coefficients, and (2) existing or assumed winds produce an
additional horizontal velocity component during descent. As a result of the horizontal
component of velocity, the area swept out during the last h, feet of fall can cause the
casualty area for any piece to be considerably larger than the casualty area obtained for
a purely vertical fall.

Figure 2 depicts two positions of a circularized flat piece, one when it is h, feet above
ground and the other at impact. A plan view is shown at the bottom of the figure, with
a side view above it.

April 13, 1995 5


b. effects of excess kinetic energy retained by the primary inert piece if perforation
occurs,
c. falling structural debris produced when the inert piece impacts on the structure.

The casualty-area modeling in subsequent sections of this report does not address these
items. Procedures for estimating inert-debris casualty areas for people in structures are
being developed in a separate study by ACTA, Inc.

4. Dimensions of a Person

In calculating casualty area, each person is assumed*to be a vertically-oriented, right
circular cylinder h, feet high with a radius of r,. Values of h, and r, are typically set to
six feet and one foot, respectively. This is obviously a compromise, since some people
are shorter and some taller than six feet, and since a person standing erect has a
cross-sectional area somewhat less than x square feet, while a person sitting or prone
occupies a greater area. Within reasonable limits, the configuration assumed for a
person is not significant, since the effects of minor variations in size or shape are
overwhelmed by the uncertainties in the overall process (e.g., the actual number of
falling pieces). All vehicle pieces are assumed to be circular with the area of each piece
equal to the pieces’s largest cross-sectional area.

With the forgoing assumptions — and no other considerations for the present — the
casualty area for a vertically falling fragment must be made larger than its cross-sectional
area to account for the dimensions of a person. The concept is illustrated in Fig. 1 where
r, is the radius of a circularized impacting fragment and r, is the radius of a person. If
the center of the fragment falls within the circle of radius (r, + r) centered at A, the
person will be hit. To put it another way, any person whose geometric center lies within
a circle of radius (r, + r,) centered at B will be hit.

April 13, 1995, 4


Appendix A. Effective Casualty Areas for Atlas IIAS Debris

Atlas IIAS debris characteristics"! are summarized in Table Al. To prepare effective
casualty areas for standard risk calculations in DAMP, impact velocities are computed
as functions of failure time. For expediency, the effective casualty areas shown in this
appendix are computed for terminal-velocity conditions instead.

Intermediate results associated with splatter calculations are given in Table A2.
Although considerable uncertainty is involved, a frangibility factor has been assigned to
each debris class. Numbers of splatter fragments and maximum splatter range are
provided for impacts on both hard and soft surfaces:

The path angles of the velocity vectors at impact are computed using the terminal
velocity as the vertical component and the mean annual wind speed for Cape Canaveral
(11.5 feet per second) as the horizontal component. The effective casualty areas for the
four effects discussed in this report are given in columns 2 through 5 of Table A3 for
hard-surface impacts, and Table A4 for soft-surface impacts. These are:

(1) Agasic: the basic effective casualty area, computed from the cross-sectional area
of the piece, the assumed dimensions of a person in the open, and the path
angle of the velocity vector at impact, discussed in Section 5,

(2) Agiae: additional casualty area from slide or skid, discussed in Section 6,
(3) Agounce? Additional casualty area from bounce or ricochet, discussed in Section 7,

(4) Axi additional casualty area from splattering and cratering, discussed in
Section 8. Splatter parameters are given in Table A2.

The composite casualty area Ag considering all four effects is given in column 6 of
Table A3 for hard surfaces, and Table A4 for soft surfaces. It is obtained by adding the
largest of the areas due to slide, bounce, and splatter to the basic area, as discussed in
Section 9.

The last column of Tables A3 and A4 shows the ratio of the composite effective casualty
area to the basic casualty area, i.e., the casualty area due to a piece falling diagonally.

April 13, 1995 54


from the origin than r, and also below height h,. With this replacement, Eqs. (37)
become

A, (splatter/piece) = > 20m = 5) ot ot ,)(Q) + st ot “| (43)
isl r

or
A, (splatter/piece) = swt * 5) 5 (ne - a + bye + al (44)
r is

where values of r, are determined from Eq. (35), w is the interval width, 1,,,. is the
maximum splatter range for pieces projected from the impacting fragment, ry is the
radius of the projected fragment, and r, is the radius of a person. The quantity Q,
depends on the relative magnitudes of d,, r,, and 1, Evaluation of Q, can be clarified by
referring to Fig. 13. For these four all-inclusive cases where the projected fragment rises
above height h,, values of Q,; are as follows:

Case 1: d; = Tp. Q, = 2d, - Tp
Case 2: d, < r,, and r; — d; 2 r,. Q, = d;
Case 3: d, <1, 4 - d,<4r,, and 7,2 4, Q=n-41,
Case 4: dj <r, 1 - dj <r, and 3, <r,. Q=0

April 13, 1995 37


in the section, consideration of multiple bounces in casualty-area evaluation seems to be
an unjustifiable complexity in view of the uncertainty in the overall process.
Consequently, RTI excludes multiple-bounce considerations in estimating effective
casualty areas for input to program DAMP.

7.9 Unequal Impact and Rebound Angles

In developing equations for A.(bounce), the assumption has been made that the impact
and rebound angles are equal. As observed from the drop tests of the irregularly-shaped
objects, these angles were generally quite different for low-velocity impacts, with the
rebound angle varying between 0° and 90°, while the ‘impact angle was kept as close as
possible to 90°. Various rebound angles are probably caused by irregularities in the
impacting and impacted bodies and by rotation of the impacting body. This suggests
that the procedures set forth in Sections 7.6 and 7.7 should be adjusted to account for
the fact that the impact and rebound angles may not be equal.

7.9.1 Density Function for Rebound Angle

Repeated trials with irregular objects seemed to show that any rebound angle between
0° and 90° was possible when the impact angle was near 90°, although higher rebound
angles occurred more frequently. As the impact velocity was increased by forceful
throws, the higher rebound angles seemed to become more likely. Although the tests
were too crude to be conclusive, it was inferred that low or intermediate impact angles
will generally produce low or intermediate rebound angles, with no rebound angle (even
backwards) being impossible. Although considerable speculation is involved, RTI has
assumed from these simple experiments that for impact angles of 90° and 0° the density
functions for the rebound angle are as shown in Fig. 7. It can be seen that the
rebound-angle density function for a 90° impact angle (, = 90°) increases linearly from
0° to 90°, while the density function for , = 0° does the reverse.

April 13, 1995 25


surface explosions scaled as the 0.4 power of the explosive weight. For rock and soil
media, the maximum distances in feet were represented as follows:

Tyyax tock) = 70 Wok. (49)
Ta (Soil) = 30 Wit, (50)

where Wyx7 is the TNT weight in pounds.

According to the same CPIA publication, page 2-18, Ahlers"! developed a similar
relationship for maximum debris range based on data from 206 accidental and planned
explosions. Applying regression-analysis techniques, he arrived at the following
relationship for maximum distance without regard for type of surface, where W yyy is in.
pounds of TNT and r,,,, is in feet.

r,,,, (explosion) = 77 W737? 61)

Equations (51) and (49) give the same answers for W = 3.4 pounds. For heavier weights,
Eg. (49) gives larger values, and for lighter weights, somewhat smaller values. Since the
composition or nature of the impacted surface is always uncertain and since most
splatter fragments are expected to come from breakup of the impacting body rather than
the impacted surface, for hard surfaces maximum splatter ranges for inert debris will be
based on Eg. (51) rather than Eq. (49). For soft surfaces, Eq. (50) is used. As mentioned
earlier, the maximum splatter distance applied in calculating the effective splatter area
— and used with the density function in Fig. 9 — is the maximum hazardous distance,
not the maximum possible distance. Since Eq. (51) gives the mean value of the
maximum projection distance, approximately half the 206 accidental explosions projected
debris to greater ranges. In part, these greater distances are due to roll or bounce that
occurred after initial impact. Since a projected piece is not as hazardous, or hazardous
at all, as it tumbles or rolls along the ground to a stop, Eq. (51) is assumed to represent
the maximum hazardous distance for debris projected from either an inert impact or an
explosion.

As stated previously, the maximum splatter distance r,,,,(splatter) is assumed to be a
function of kinetic energy per unit area. It is further postulated that r,,,,(splatter) is
equal to r,,.(explosion), where r,,.,(splatter) is calculated from Eq. (51) after impact
kinetic energy has been scaled and then converted into equivalent pounds of TNT. If
Winr is proportional to KE/A, then

wv? ft-lb 11b TNT (52)
x
2gA ft? 1.54% 10° ft-lb

Wyyy(lb) ©

April 13, 1995 42


equation for A{bounce), overlapping areas must not be counted twice. The left half of
the fragment at first impact is excluded, since it has already been included in the basic
casualty area from Eq. (4); and the right half of the fragment at first impact is cancelled
by omitting the right half of the fragment at second impact. If the duplicated area A is
then subtracted, the equation for A{bounce) becomes

A (bounce) = 2{c, + r,)d + n(r, + ry +2(r, + r,)d -A (26)

= 4d(, + r,) + n(r, + r,) -A
7.8 Multiple Bounces

The information presented so far in Section 7 does not address the possibility of multiple
bounces. In view of the potential error in estimating coefficients of restitution for
irregular components impacting in unknown attitudes on uncertain surfaces,
consideration of multiple bounces may seem like “overkill”.

From Table 7 the highest first bounce on a hard surface occurs for a piece having a
ballistic coefficient of 10 Ibs/ft? and a terminal velocity of 93.6 ft/sec. The data in
Table 8 have been computed to show, theoretically at least, bounce heights and distances
for the first five bounces of that object. Although, in theory, bouncing would continue
forever, it seems apparent that a practical limit would be reached after one or .two
bounces.

Table 8. Multiple Bounce Heights and Distances on Hard Surfaces

B = 10 Ibs/ft?, V; = 93.6 ft/sec
Vertical | Horiz. Total Coef. Total
Bounce | impact | impact | impact of rebound | Bounce | Bounce
No. velocity | velocity | velocity | resti. | velocity | height | distance
(ft/sec) | (ft/sec) | (ft/sec) e (ft/sec) (ft) (ft)
1 93.6 11.5 94.3 0.287 27.0 11.19 5.50
2 26.8 3.3 27.0 0.500 13.5 2.80 1.38
3 13.4 1.6 13.5 0.500 6.8 0.70 0.34
4 6.7 0.8 6.8 0.500 34 0.17 0.09
5 34 04 34 0.500 17 0.04 0.02

For this worst-case example from Table 8, the second-bounce height is only 2.8 feet, well
below the height of a person. Thus, in estimating the additional casualty area caused
by any bounce after the first, low-bounce procedures apply. However, as stated earlier

April 13, 1995 24


Table B2. Delta-GEM Splatter Parameters

KE/A Frangible | Mean wt. | Num. Splat. Frags Ryax (ft)
(feIb/fe) | factor Mb) | Hard | soft | Hara | Soft
10.0 0.1 0.8 0.0 0.0 14 0.2
67.9 0.2 15 0.1 0.1 2.6 0.4
258.3 0.2 5.1 0.3 0.3 4.0 0.8
3,816.4 0.3 5.4 0.3 03 95 2.2
1524.2 0.2 0.9 0.1 0.1 7.0 15
1,242.2 0.4 10.6 14 1.7 6.6 14
5,084.7 04 3.4 05 05 10.4 2.5
7,094.8 05 11 0.2 0.2 11.6 2.8
8,241.3 05 83 14 14 12.1 3.0
39,444.5 0.6 2.0 04 04 20.1 5.6
10,401.7 04 3.7 0.8 0.8 13.1 3.3
45,7743 0.5 23.7 83 73 21.1 6.0
31,184.8 0.4 47 13 11 18.6 5.1
D15 53,529.3 1.0 2.4 14 12 22.1 64
D16 313,061.8 0.5 22.9 10.6 8.0 39.1 12.9
D17 22,6629 1.0 22.5 11.1 103 16.8 45
D18 1,678.6 0.2 34 0.3 03 73 1.6
D19 7,018.1 03 76 11 11 115 2.8
D20 4,333.9 0.2 23 0.6 0.7 99 2.3
D21 4,353.9 0.2 0.9 0.2 03 99 23
D22 24,101.8 0.5 19 0.8 0.7 17.1 46
D23 81,158.9 1.0 3.4 21 17 25.3 7.5
D24 41,763.6 03 11.9 25 2.2 20.4 5.8
D25 * 107,302.8 1.0 48.7 43.9 36.1 27.7 8.4
D27* 987,302.7 1.0 84.9 113.4 78.4 56.6 | 205
GP1* 76,955.1 1.0 1.7 1.6 0.0 24.9 0.7
GP2 * 12,119.8 1.0 03 0.2 0.0 13.7 0.7
GP9 * 221,877.6 1.0 7.2. 5.2 13 35.0 74
233.5 0.0 1.2 0.0 0.2 3.8 3.5
231.7 0.0 29 0.0 4.0 3.8 | 113

* Data for these classes taken at 20 seconds

April 13, 1995

61


Casualty Areas from Impacting Inert Debris for People in the Open
1. Introduction

When a missile or space vehicle malfunctions, people and facilities may be subjected to
significant risks from falling inert debris, or from overpressures and secondary debris
produced by a stage, component, or large propellant chunk that explodes on impact.
Although risks are greatest in the launch area and along the intended flight line, lesser
risks exist throughout the area inside the impact limit lines, and even outside if the flight
termination system should fail or other unlikely events occur. In accordance with
contractual tasking, the purpose of this study is fo develop analytic models for
estimating casualty expectancy from primary (impacting) and secondary (projected) inert
debris for people in the open. As used here, primary debris consists of non-explosive
vehicle components and pieces that fall to earth following a vehicle malfunction.
Secondary debris consists of inert vehicle fragments and crater materials projected
outward from impacting components. Damage to facilities and injuries to people from
explosive overpressures have been treated in a companion document", "Facility
Damage and Personnel Injury From Explosive Blast". Although fire, toxic materials, and
radiation may also subject personnel to significant danger, these hazards are not
addressed in Ref. [1] or in this study.

2. Casualty Expectancy
2.1 The Casualty Expectancy Concept

If inert vehicle pieces impact in an area or region of constant population density, the
expected or average number of casualties can be calculated from the so-called casualty-
expectancy equation,

A
E, = P,xNx— (1)
. A

where E, is the expected number of casualties, P; is the probability of impact in the
region, N is the number of people in the region, A, is the total effective casualty area for
the impacting pieces, and A is the area of the region. This equation, which is also
applied when the population density is unknown or random, is used to calculate the
expected number of casualties to people in the open from impacting inert debris. The
actual calculation of casualty expectancy is considerably more involved than might be
inferred from Eg. (1), since calculations must be summed statistically over all failure
modes and time intervals for all pieces in each debris class and for all classes of debris.

It should be noted that E, is not the probability of a casualty. The distinction between
casualty expectancy and probability of casualty can be clarified by a simple numerical
example: Assume for some vehicle system that one test in 1000 is expected to result in

April 13, 1995 1


Table 5. Bounce Heights

Height of Bounce (ft) |
B Vr
(Ibs/ft?) | (ft/sec) | e = 0.05 | e=01 | e=0.2 | e=03 | e=04 | ce = 06
0.2 13.2 0.01 0.03 0.11 0.24 0.43 0.97
05 20.9 0.02 0.07 0.27 0.61 1.09 2.44
1.0 29.6 0.03 0.14 0.54 1.22 2.18 4,90
2.0 41.8 0.07 0.27 1.09 2.45 4.35 9.79
5.0 66.2 0.17 0.68 2.72 6.12 10.9 24.5
10.0 93.6 0.34 1.36 5.44 12.2 21.8 49.0
20 132.3 0.68 2.72 10.9 24.5 43.5 97.9
50 209.2 1.70 6.80 27.2 61.2 109. 245.
100 295.8 3.40 13.6 54.4 122. 218. 490.

From inspection of Table 5, a body with B = 1.0 and e = 0.3 that impacts at 29.6 ft/sec
would bounce about 1.2 feet high. Since to acquire this velocity such a body must fall
from a height of at least 14 feet, a 1.2-foot-high bounce does not seem unreasonable. At
the other extreme, a body with B = 100 and e = 0.3 impacting at a terminal velocity of
295.8 ft/sec would, according to the bounce equations, rebound 122 feet. This bounce
height seems unreasonable, since a vehicle component impacting at this speed would
surely shatter while producing a crater, or bury itself into or under the surface, or be
flattened almost beyond recognition. In fact, it does not seem credible that vehicle
components impacting at speeds of several hundred feet per second will remain
essentially intact, and thus produce bounce, as defined in this report. (The added
casualty area produced by the splattering of pieces from high-speed impacts is discussed
later in Section 8.)

7.4 Estimates of Low-Velocity Coefficients of Restitution

As a further crude guide in estimating low-velocity values of e, several objects were
dropped from a balcony onto a concrete sidewalk and then onto a weedy dirt surface.
Items dropped from a height of about 9 feet included a fully-inflated basketball, a
standard softball, a tennis ball, a small wood block, a steel bolt with flange nut attached,
and a thin steel cup-like object with a small hole in the bottom. For the three balls,
height of bounce was measured (within an inch or so), and the coefficient of restitution
calculated from the equation

April 13, 1995 15


8.10 Attempt to Obtain Experimental Data

The results obtained using Eqs. (53) and (51) to establish maximum splatter ranges for
impacting inert bodies are admittedly subject to considerable uncertainty. A similar
statement can be made about the use of Eqs. (58) and (55) to estimate numbers and
mean weights of splatter pieces. In an effort to obtain experimental data on which to
base assumptions and thus increase confidence in the results, RTI wrote to the National
Transportation Safety Board requesting information on debris scatter from high-speed,
near-vertical, non-explosive, aircraft impacts. In response'”!, NTSB provided
information on seven accidents where the aircraft impact angles varied between 45°
and 85°. Three of the seven had estimated impact angles between 80° and 85° with
impact speeds from 363 ft/sec to 507 ft/sec. The numbers of pieces with recorded
locations varied from 39 to 114 with no weights given. A study of the debris diagrams
from these latter three accidents showed that aircraft parts and pieces were scattered
several hundred feet from the main-body impact craters. Additional information about
the crashes, such as the following, are needed if the data are to be useful in estimating
splatter parameters:

. Aircraft heading just before and at impact

. Aircraft breakup or breakaway of pieces before impact

. Extent to which scatter of pieces was due to effects of winds after impact, or to
pieces tumbling down inclines.

. Extent to which pieces were scattered by a deflagration at impact

. Wind speed and direction after impact before piece locations were recorded
Characteristics of dispersed pieces

. Weights and total numbers of pieces

oD

namo

Since the needed information was not provided and seems unlikely to be forthcoming,
the data provided by the NTSB has not been used in formulating splatter-model
parameters. If information on these or other accidents or incidents should become
available in the future, procedures for modeling splatter parameters should be revisited.

April 13, 1995 52


Appendix B. Effective Casualty Areas for Delta Debris

Delta-GEM debris characteristics!” are summarized in Table B1. To prepare
effective casualty areas for standard risk calculations in DAMP, impact velocities are
computed as functions of failure time. For expediency, the effective casualty areas
shown in this appendix are computed for terminal velocity conditions instead.

Intermediate results associated with splatter calculations are given in Table B2.
Although considerable uncertainty is involved, a frangibility factor has been assigned to
each debris class. Numbers of splatter fragments_and maximum splatter range are
provided for impacts on both hard and soft surfaces.

The path angles of the velocity vectors at impact are computed using the terminal
velocity as the vertical component and the mean annual wind speed for Cape Canaveral
(11.5 feet per second) as the horizontal component. The effective casualty areas for the
four effects discussed in this report are given in columns 2 through 5 of Table B3 for
hard-surface impacts, and Table B4 for soft-surface impacts. These are:

(1) Ajagc: the basic effective casualty area, computed from the cross-sectional area
of the piece, the assumed dimensions of a person in the open, and the path
angle of the velocity vector at impact, discussed in Section 5,

(2) Agige: additional casualty area from slide or skid, discussed in Section 6,
(3) — Arounce: Additional casualty area from bounce or ricochet, discussed in Section 7,

(4) Axa? additional casualty area from splattering and cratering, discussed in
Section 8. Splatter parameters are given in Table B2.

The composite casualty area A. considering all four effects are given in column 6 of
Table B3 for hard surfaces, and Table B4 for soft surfaces. It is obtained by adding the
largest of the areas due to slide, bounce, and splatter to the basic area, as discussed in
Section 9.

The last column of Tables B3 and B4 shows the ratio of the composite effective casualty
area to the basic casualty area, i.e., the casualty area due to a piece falling diagonally.

April 13, 1995 59


Since the area under f(r) must be unity, the constant A = 2/r,,.,, and

f) = 2-9 (33)

r
‘max

8.3 Casualty Area for Fixed Splatter Range With No Overflight

Even if a splatter fragment is projected directly toward a person with sufficient velocity
to reach or impact beyond the person, he or she would not be hit if the fragment passes
overhead. For the moment, however, the possibility of overflight will be neglected.
Instead, the simplifying assumption is made that a fragment projected in the proper
direction with sufficient range will score a hit, with this latter condition being equivalent
to the assumption that the fragment trajectory never rises above h, feet. The effective
(or average) casualty area for the fragment will now be evaluated for this case.
Figure 10 is a ground-plane depiction of a projected fragment that impacts at distance r
from the origin (edge of impacting piece).

(ort 'p)
_ person

impacting
piece projected
fragment

Figure 10. Casualty Area for Splatter Fragment

It is apparent from the figure that a person located on either side of the center line of
travel of the projected fragment within a distance of (r,¢+ r,) will be hit. For this
particular impact range r, the effective casualty area becomes approximately

April 13, 1995 32


A. (fixed splatter range) ~ lc ot x) (r - r,) + sid + 1) (34)

2

In the second pair of parentheses, r, is subtracted from r to avoid duplication of an area
already accounted for by the second term in Eq. (4). Since Eq. (34) applies for a single
fixed splatter range r, it serves only to introduce basic concepts. The calculation of
effective casualty area must account for the fact that the projected fragment can impact

anywhere out to range r,,,, in accordance with the density function shown in Fig. 9.
8.4 Casualty Area for All Range Intervals With No Overflight

Now consider Fig. 11 where the distance r,,,, has been divided into n equal intervals, one
such interval being shown as shaded in the figure. The interval width w is simply
Tinax/ N-

t,

max

edge of impacting fragment

Figure 11. Splatter-Range Density-Function Interval

The distance, r,, from the origin to the midpoint of interval i is

r= [=f - H isten (35)
, n 2

April 13, 1995 33


Table 16. Percent of Explosive Energy Converted into
Fragment Kinetic Energy

Accident Vehicle/Stage | Energy Converted to KE (%)
Atlas Centaur 0.14
S-IVB-ASTV 0.18
S-IV-EAFB 0.31
S-IVB-503 0.13
Mean 0.19

The following assumptions will now be made:

(1) If the impacting body weighs less than 0.25 pounds, the splatter effect is
negligible (zero).

(2) For hard surfaces, the percentage of the kinetic energy of an impacting inert
body that is transferred to the splatter fragments is 0.095%. This is half the
estimated mean percentage of explosive energy that was converted into kinetic
energy in projecting fragments from the four explosions listed in Table 16. For
soft surfaces, the percentage of energy transferred to the splatter fragments is
one-fourth that for hard surfaces.

(3) The weight of the heaviest possible projected piece is equal to the weight of
the impacting body. The weight of the smallest, hazardous, projected piece
is 0.25 pound.

(4) The number of projected pieces is normally distributed with respect to the
natural logarithm of piece weight, with the logarithms of the maximum and
minimum weights, as defined in assumption (3), considered to be + 3-sigma
values. The weight of the mean projected piece thus becomes

ss Wx * log, vs] (55)
Worcan = EXP]

The average KE required to project the mean piece to ranges between zero and
Tmax(Splatter) can now be calculated for any impacting body. Referring to the density
function [f(r)] in Fig. 9, the distance r,,,, is divided into n intervals. For each interval,
the kinetic energy needed for the mean splatter piece to reach the midpoint of the
interval is calculated for initial projection angles of 15°, 30°, 45°, 60° and 75°. The mean
of the five KE values is computed and designated as KE(mean). Because splatter ranges

April 13, 1995 48


(1) (2) @) (4)

Position at Position at Position at

first impact . . second impact

Figure 5. Plan View for Long-Bounce Fragment
From Fig. 5 it can be seen that
d,2d+(t,+r)+(t, +1) +d =2(d +4, +1) (19)

where d, is the total bounce distance on the first bounce, and d is the horizontal distance
traveled while the fragment rises to height h,, and again while it falls from height h,.
The time to reach height h, during the first bounce can be calculated from the equation

_ v, sing + (v, sing)” - 2gh, (20)
, &

where v, is computed from Eq. (7) and from Eq. (8). (If the radicand in Eq. (20) is
negative, the bouncing fragment does not reach height h,.) The distance d in Fig. 5 is
calculated from

April 13, 1995 21


Te = 5.13 + 6.87 l0g,, Wioan

(59)

Using this equation produces the projected-fragment sizes shown in Table 17.

Table 17. Sample Projected Fragment Sizes

Mean Piece Projected Fragment
Weight (Ib) Radius (inches)
0.25 . 1.00
1 5.13
3 8.41
10 12.0
30 15.3
100 18.9
300 22.1
1000 25.7

Using the procedures outlined in this section and the Atlas ILAS components listed in
Table 10, the maximum splatter range, number of splatter fragments, and mean
splatter-fragment weight and radius are shown in Table 18. Although the number of
splatter fragments can be made integral, fractional numbers can be used in the risk

calculations.

Table 18. Sample Splatter Parameters for Hard-Surface Impacts

Max Splatter | Number of | Mean Splatter | Mean Splatter

Range Splatter Frag Weight Fragment
Atlas TAS Components (f0) Fragments (Ib) Radius (in)
Turbo-pump assembly 40.3 16.2 16.2 13.4
Expended Castor IVA 35.8 115 19.7 14.0
Centaur engine assembly 17.0 6.7 10.5 12.1
Interstage adapter 81 4.7 17.4 13.6
Jettison rail 5.3 08 2.9 8.3

April 13, 1995 51


Table B1. Delta-GEM Debris Characteristics

Weight | Cross-sect. | Subsonic | Terminal Vel.
Class | Description (Ib) Area (ft?) | B (Ib/ft’) (ft/sec)
D2 Miscel. Delta frags 2.28 3.20 0.88 278
D3 Miscel. Delta frags 9.20 4.83 2.47 46.5
D4 Propellant tank frags 104. 26.02 4.60 63.5
D5 Fairing, skirt, etc. 117. 3.57 8.41 85.8
D6 Miscel. Delta frags 3.41 0.28 9.05 89.0
D7 Nosecone fairing 448. 52.25 10.50 95.9
D8 Miscel. Delta frags 45.4 2.10 17.14 122.5
D9 Miscel. Delta frags 4.97 0.17 17.69 124.4
D10 Miscel. Delta frags 273. 8.53 18.78 128.2
D11 Miscel. Delta frags 16.0 0.17 30.66 163.8
D12 Small tanks, nozzle 56.0 2.58 35.08 175.2
D13 RS-27 Stage I engine 2242. 46.67 69.90 247.3
D14 Miscel. Delta frags 87.3 2.26 59.20 227.6
D15 Miscel. Delta frags 22.2 0.34 60.12 229.4
D16 Apogee kick motor 2095. 15.57 170.90 386.8
D17 Payload 2023. 47.78 39.20 185.2
D18 AI GEM noz. closure 47. 5.58 14.50 112.7
D19 GEM nosecone 230. 11.39 25.40 149.1
D20 GEM fwd. dome frags 21. 4.36 66.00 240.3
D21 GEM skirt frags 3. 0.62 66.00 240.3
D22 GEM igniter boss 15. 0.56 66.00 240.3
D23 GEM propellant frags 45. 0.56 74.10 254.7
D24 GEM nozzle assembly | 564. 12.28 66.70 241.6
D25* | Thrusting GEM 9501. 142.30 118.00 321.4
D27* | Unignited GEM 28839. 142.30 358.00 559.8
GP1* | GEM prop. frags 11. 0.22 | 113.00 3144
GP2* | GEM prop. frags 0.4 0.02 44.40 197.1
GP9* | GEM non-burn prop. 205. 151 120.00 324.1
GCl1 GEM Case frags 5A 1.40 4.30 61.3
GC2_ | GEM Case frags 33.1 8.65 4.30 61.3

* Weights for these classes taken at impact following failure at 20 seconds

April 13, 1995

60



Abstract

Ina typical missile or space-vehicle risk study, a significant portion of the risk is due to
falling inert debris. The report presents methods and procedures for estimating the
casualty areas for such debris for people in the open, but not for people in houses, office
buildings, or other structures.

After discussing what constitutes a hazardous piece and presenting the equation for
computing casualty expectancy, detailed methods are provided for evaluating the basic
casualty area for an impacting piece. This area depends on the cross-sectional area of
the piece, the assumed dimensions of a person in the open, and the path angle of the
velocity vector at impact. Other augmenting effects that can cause the casualty area of
an impacting piece to be considerably larger than the basic casualty area of the piece
itself are also discussed. These are:

a. slide or skid
b. bounce or ricochet
c. splattering and cratering

A procedure for arriving at a composite casualty area to substitute in the
casualty-expectancy equation is provided.

Casualty areas for inert debris produced by breakup of the Atlas ITAS and Delta-GEM
vehicles are given in appendices.

April 13, 1995 i


If for the i'* interval, A,(max) is less than N times the casualty area for a single projected
piece, A,(max) is substituted instead for the last bracketed term in Eq. (43).

Equation (44) or Eq. (43) gives the effective casualty area for a single projected piece.
The issue of the number of pieces projected from an impacting component is discussed
later in Section 8.7. If N pieces are projected, each term in Eq. (43) must be multiplied
by N or replaced by A(max). The total casualty area due to splatter for the component
may then be represented by the equation

n

A, (splatter/component) = > (Maximum of [N A, (splatter/piece),, A(may)]) (47)

isl

As a modification to the foregoing, there is some minimum velocity that a projected
piece must acquire before it is considered hazardous. According to data presented by
Ahlers”!, the threshold for serious injury for one to two-pound pieces is about
15 feet/second. Lighter pieces require greater velocities to do serious injury, while
pieces heavier than about two pounds need slightly less than 10 feet/second. Although
somewhat arbitrary, for use in computing effective splatter areas a threshold velocity of
10 feet/second (corresponding to a maximum impact distance of 3.1 feet) has been
selected. This velocity is acquired by the piece in falling from a height of 1.6 feet. Thus,
if a piece is projected at a velocity so low that it cannot impact more than 3.1 feet from
the periphery of the impacting fragment, the effective splatter area is assumed to be zero
for the projected piece. To put it another way, if r,,,. for an impacting piece is less than
3.1 feet, the splatter area for that piece is zero.

8.6 Maximum Splatter Range

Before the effective splatter area (i.e., the casualty area due to splatter) can be evaluated
for an impacting component, the maximum splatter range r,,, and the number of
splatter pieces must be established for the component. To a large extent, the maximum
hazardous splatter range for an impacting inert component is a matter of engineering
judgment. It seems reasonable to assume that it is some rather complicated function of
kinetic energy per unit area (rather than kinetic energy), although many imponderables
exist, e.g., shape, mass, orientation, and composition of the impacting component, impact
velocity, properties of the impacted terrain, energy lost in cratering and in crumpling
and tearing apart the impacting component. In impact experiments with steel
spheres"! where both the impacting and impacted materials were fairly reproducible,
the results varied a great deal. Depth of penetration, for example, was not predictable
to better than a factor of two even when projectile parameters and impacted materials
were well known. The following is quoted from Section III of Ref. [10], which discusses
the non-predictability of the effects of impact:

April 13, 1995 40


Ny posrrnrrg ‘aaa ccc
P | Case (1) :

Figure 13. Fragment Trajectory Geometry

April 13, 1995 38


Table B4. Delta-GEM Effective Casualty Areas for Soft-Surface Impacts

[—T
Avasic Agiae Avounce Agpat Ag Ratio
Class (ee) GD) a) fe) (fe) Mead vase
D2 22.67 11.80 4.84 0 34.47 15
D3 22.41 13.15 13.23 0 35.64 1.6
D4 55.68 22.77 36.06 0 91.74 1.6
D5 16.73 12.13 18.79 0 35.53 21
D6 7.31 7.63 11.62 0 18.93 2.6
D7 88.33 29.82 43.37 .0 131.70 15
D8 12.43 0 11.19 0 23.61 19
D9 6.14 0 7.33 0 13.47 2.2
D10 24.87 0 14.66 0 39.54 1.6
Di11 5.81 0 2.21 2.08 8.02 14
D12 12.92 0 1.70 3.04 15.95 12
D13 76.74 0 0 18.90 95.63 1.2
p14 11.85 0 0 6.70 18.55 1.6
D15 6.35 0 0 7.93 14.27 2.2
D16 33.85 0 0 87.57 121.43 3.6
D17 79.08 0 1.60 10.77 89.84 11
D18 19.95 0 16.68 0 36.64 18
b19 29.18 0 9.42 0 38.60 13
D20 16.15 0 0 0 16.15 1.0
D21 7.38 0 0 0 7.38 1.0
D22 7.17 0 0 3.52 10.69 15
D23 7.13 0 0 14.37 21.49 3.0
D24 29.54 0 0 14.04 43.58 15
D25 * 191.05 0 0 37.36 228.41 1.2
D27 * 189.63 0 0 213.29 402.93 21
GP1* 5.58 0 0 9.96 15.54 2.8
GP2* 442 0 0.01 0.57 4.99 11
GP9 * 9.73 0 0 49.57 59.30 6.1
Gcl 12.49 9.79 15.40 0 27.88 2.2
GC2 28.20 15.62 24.56 0 52.76 1.9
iL ——

* Data for these classes taken at 20 seconds

April 13, 1995



moving body travels before coming to 1
equations found in elementary physics boo!

F = -fw
»- (ah
Ww
Fan
a
d etaee

5 2

est can be computed from the following
ks:

-fg
y, (5)

h

Wy
v,f = =|—
2\fg

aq

where F is the frictional force, f is the coefficient of friction, w is the body weight, a is
the horizontal acceleration, g is the acceleration due to gravity, t is the time required to
bring the sliding body to rest, v, is the initial horizontal velocity, and d, is the slide

distance.

6.2 Slide Coefficients and Distances

Typical values for the coefficient of sliding friction between various pairs of materials

are shown in Table 2"). Coefficients coul
concrete, blacktop, or gravel.

id not be found for metals on sand, shell,

Table 2. Coefficients of Sliding Friction

Coefficient
Materials of Friction, f
masonry on brickwork 0.60 to 0.70
wood on wood 0.25 to 0.50
iron on stone 0.30 to 0.70
wood on stone 0.40
metals on oak 0.50 to 0.60
metals on metals 0.15 to 0.30
masonry on clay 0.33 to 0.51
earth on earth, gravel 0.81 to 1.11

Table 3 shows slide distances for six values of f for initial horizontal velocities up to 25

ft/sec. It is apparent that the casualty ar
velocity component at impact.

ea due to slide depends on the horizontal

April 13, 1995 8


8.8 Frangibility Factor

As mentioned earlier, the number of splatter fragments produced by an impacting body
depends on its composition since a module, instrumentation section, or fragile payload
consisting of many components would presumably produce more splatter fragments
than, for example, a rigid helium sphere. This presumption is at least partially
confirmed by a report"! that shows pictures of helium spheres and other rigid
components that have survived both orbital reentry and impact essentially intact.

To account for compositional differences in impacting bodies, Eq. (57) has been modified
as shown in Eq. (58) by the inclusion of a frangibility factor f that varies between zero
and one. A value of f = 1 is assigned to a body that is considered highly frangible,
while f = 0 is used for a body that is not expected to break up or project debris after
impact. Bodies of intermediate frangibility are, of course, assigned intermediate values.

- (£) (F) (KE of impacting body) (58)
KE(mean projected fragment)

Although inclusion of a frangibility factor in the equation for N seems logically sound,
some procedural problems arise in application:

a. The composition of pieces resulting from vehicle breakup may not be known
sufficiently well to make realistic choices for f.

b. Another consideration - in addition to ballistic coefficient, breakup velocity,
weight, and area — is introduced in classifying breakup debris. Thus it may be
necessary to split debris that is now placed in a single class into two or more
classes.

In view of practical problems, a value of f = 0.5 is used to develop casualty areas for
splatter when knowledge of debris composition or the results of impact are too uncertain
to permit a logical choice for f.

8.9 Size of Splatter Fragment

As seen from Eg. (44), the radius of the projected fragment r,; is needed to calculate
effective casualty area. Since some value or relation must be established, it seems
reasonable to assume that r,- is proportional to fragment weight, or rather to the mean
weight of all fragments projected from the impacting body. Remembering that the
weight of the largest projected piece is assumed to be the weight of the impacting body
and the weight of the smallest piece is 0.25 pounds, a linear relationship was established
between the radius of the mean piece and the logarithm (base 10) of its weight. The
smallest piece was assumed to have a radius of one inch, while a piece weighing
10 pounds was given a radius of 12 inches. In equation form, the relationship becomes:

April 13, 1995 50


Table A2. Atlas IIAS Splatter Parameters

KE/A Frangible | Mean wt. | Num. Splat. Frags Ranax (ft)
Class (ft-Ib/ft?) factor (Ib) Hard Soft Hard | Soft
Al 13.0 0.1 0.9 0.0 0.0 15 0.2
A2 15.0 0.2 19 0.1 0.1 1.6 0.2
A3 21.7 0.1 1.2 0.0 0.0 18 0.3
A4 30.3 0.2 21 0.1 0.1 2.0 0.3
AS 37.7 0.1 1.0 0.0 0.0 21 0.3
A6 76.6 0.1 0.0 0.0 0.0 2.7 0.5
A7 87.1 0.8 3.4 0.6 0.8 2.8 0.5
A8 476.4 0.5 11 0.1 0.2 48 1.0
AQ 333.6 0.5 0.7 0.1 0.1 4.3 0.8
A10 360.1 0.5 2.8 0.4 0.4 4A 0.9
All 922.1 0.2 1.7 0.1 0.1 6.0 13
Al2 4,139.1 04 21.8 1.9 2.0 9.7 2.3
Al3 1,630.9 0.5 11 0.2 0.2 7.2 1.6
Al4 2,237.4 05 7A 1.2 14 8.0 1.8
Al5 2,723.1 0.4 18 0.3 0.3 8.5 1.9
Al6 8,563.1 0.5 15 0.3 0.3 12.3 3.1
A117 9,916.6 0.5 0.6 0.1 0.1 12.9 3.3
Al18 7,966.8 0.2 3.2 03 0.3 12.0 3.0
Al19 18,099.0 09 17.6 7.7 73 15.6 41
A20 13,597.5 0.4 4.0 1.0 1.0 14.2 3.7
A21 24,004.0 0.8 8.9 44 Al 17.1 4.6
A22 139,633.1 0.5 1.0 0.4 0.3 30.2 9.4
A23 137,051.1 0.5 3.3 1.2 0.9 30.0 9.3
A24 343,994.1 0.7 16.2 11.3 85 40.3 13.4
P1 44.5 0.2 2.5 0.1 0.1 2.3 0.4
P2 623.7 0.6 5.6 0.6 0.7 5.3 11
P3 7 A87.7 0.8 16.7 3.5 3.6 11.8 2.9
P4 6,200.2 08 46 1.1 11 11.1 2.7
PS 480,528.6 0.8 36.6 25.9 19.0 44.9 15.3
Cl 59.6 0.2 1.2 0.0 0.1 2.5 0.4
C2 275.7 01 15 0.0 0.1 41 0.8
C3 716.8 0.6 3.2 0.5 0.6 5.5 11
C4 6,613.4 05 1.0 0.3 0.3 11.3 2.8
(es) 41,000.6 0.3 4.0 0.9 0.8 20.3 5.7
C6 * 108,668.8 1.0 1.0 21 18 27.8 8.5
C7* 167,286.3 1.0 1.0 3.2 2.6 32.0 10.1
C8 * 1,010,605.6 1.0 60.0 123.2 85.0 57.0 20.7
C9 * 2,351,357.1 1.0 74.0 176.9 114.3 74.9 29.0
C10 * 918,013.6 1.0 58.6 118.3 82.2 55.3 19.9
Ccl1* 2,302,726.9 1.0 73.7 175.3 113.4 74.4 28.7

* Data for these classes taken at 20 seconds

April 13, 1995

56



shell, or rock. So that the casualty areas due to slide will not be underestimated, the
following assumptions have been made:

(1) _ The vertical component of velocity after impact is zero.
(2) The horizontal component of velocity is unchanged by impact.

(3) For all fragments, the average coefficient of friction f is 0.5 for slides on hard
surfaces, corresponding to the mid-range value shown in Table 3 for iron on
stone. For slides on soft surfaces f is 0.7, a value at the lower end of the range
for earth on earth or gravel. .

(4) _ If the vertical component of impact velocity exceeds 100* feet per second, the
impacting body will not slide, and the casualty area due to slide is zero.

(5) The slide distance can be evaluated using Egs. (5) when the vertical
component of impact velocity is less than 100 feet per second. The computed
sliding distance is interpreted to mean the maximum hazardous distance
rather than the maximum possible distance.

* At vertical velocities exceeding 100 feet per second, an impacting body is expected
to break up, bounce, or dig into the surface rather than slide. As defined in this
report, these events are mutually exclusive.

April 13, 1995 10


Form Approved

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1. AGENCY USE ONLY (Leave blank) ‘apn 3 7036 arene TYPE AND DATES COVERED
4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
Casualty Areas from Impacting Inert Debris for People in the Open C: FO4703-91-C-0112
TA: 10/94-60

“Robert NM Montgomery
James A. Ward, Jr.

"7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
Research Triangle Institute* ACTA, Inc.** . REPORT NUMBER
3000 N. Atlantic Avenue Skypark 3 RTI/5180/60-31F
Cocoa Beach, FL 32931 23430 Hawthorne Blvd., Suite 300

Torrance, CA 90505

‘9. SPONSORING/ MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING / MONITORING
Department of the Air Force (AFSPC) AGENCY REPORT NUMBER
30th Space Wing 45th Space Wing
Vandenberg AFB, CA 93437 Patrick AFB, FL 32925

Mr. Martin Kinna (30 SW/SEY) Louis J. Ullian, Jr. (45 SW/SED)

11, SUPPLEMENTARY NOTES
* Subcontractor

“Prime Contractor

‘2a. DISTRIBUTION / AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE
Distribution authorized to US Government agencies and their contractors to protect
administrative/operational use data, 13 April 95. Other requests for this document shall be referred
to the 30th Space Wing (AFSPC) Directorate of Safety (30 SW/SE), Vandenberg AFB, CA 93437,
or 45th Space Wing (AFSPC), Directorate of Safety (45 SW/SE), Patrick AFB, FL 32925.

13. ABSTRACT (Maximum 200 words)
In a typical missile or space-vehicle risk study, a significant portion of the risk is due to falling inert debris. The
report presents methods and procedures for estimating the casualty areas for such debris for people in the open,
but not for people in houses, office buildings, or other structures.

After discussing what constitutes a hazardous piece and presenting the equation for computing casualty expectancy,
detailed methods are provided for evaluating the basic casualty area for an impacting piece. This area depends
on the cross-sectional area of the piece, the assumed dimensions of a person in the open, and the path angle of
the velocity vector at impact. Other augmenting effects that can cause the casualty area of an impacting piece to
be considerably larger than the basic casualty area of the piece itself are also discussed. These are: slide or skid,
bounce or ricochet, splattering and cratering. A procedure for arriving at a composite casualty area to substitute
in the casualty-expectancy equation is provided. Casualty areas for inert debris produced by breakup of the
Atlas IIAS and Delta-GEM vehicles are given in appendices.

14. SUBJECT TERMS 15. NUMBER OF PAGES
inert launch-vehicle debris, casualty area 71

16. PRICE CODE

77. SECURITY CLASSIFICATION | 18. SECURITY CLASSIFICATION | 19. SECURITY CLASSIFICATION | 20. LIMITATION OF ABSTRACT
REPORT

OF OF THIS PAGE OF ABSTRACT
Unclassified Unclassified Unclassified SAR
NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. 239-18
298-102


(1) the person is located along the radial line of travel of the projected
fragment,

(2) the person is within the range interval traversed by the fragment when the
fragment is within h, feet of the ground.

8.2 Splatter-Range Density Function

As a first step in deriving an effective casualty area for projected splatter fragments, a
splatter-range density function will be established. In deriving the function, the
assumption is made that the impact probability for each projected fragment decreases
linearly from the point of piece impact out to some maximum impact range fina, beyond
which the probability is zero. (The rationale for this assumption and its consequences
are given in Section 4.3.2 of an earlier RTI report!) The term ‘maximum impact
range’, as used here, means the maximum hazardous distance (rather than the maximum
possible distance) from the edge of the impacting piece. Although a fragment may roll
or bounce somewhat farther than this, it would not be considered hazardous beyond this
range since its velocity would be low and dropping to zero. The assumed function is
shown in Fig. 9, where r,,., is the maximum hazardous distance measured from the edge
of the impacting piece, and A is a constant to be determined. Methods for estimating
numerical values for r,,,, are given in Section 8.6.

i(r)

4 Frax)
edge of impacting piece

Figure 9. Splatter-Range Density Function

April 13, 1995 31


reasonable bounce heights for the assumed range of impact velocities. Since
the relationship between e and velocity involves considerable speculation, the
assumption of a log function seems as good as any other.

(d) The assumed relationships establish upper limits for impact velocities that can
produce bounce. Beyond these limits, the body is assumed to break apart or
bury itself, thus producing splatter and no bounce. A smaller limiting velocity
is chosen for soft surfaces than for hard, since the kinetic energy for a
soft-surface impact is more likely to be consumed by the body in producing
a crater and in burrowing into the ground,

For values of Vp above 300 feet per second (hard surfaces) or 200 feet per second (soft
surfaces) where e = 0, breakup of the body upon impact or digging into the ground
precludes bounce as defined here. The fragments of an impacting body that do in fact
bounce are considered to be splatter fragments. Casualty areas for those fragments are
evaluated as described later in Section 8.

Using the assumed relationships for e and a mean annual wind speed for Cape
Canaveral of 11.5 ft/sec", bounce distances and heights were calculated for terminal
velocities V; of impacting components having various values of B. Results are given in
Table 7 for both hard and soft surfaces.

Table 7. Bounce Distances and Heights

B Vy e Horizontal Bounce Bounce Height
(Ibs/ft?) | (ft/sec) Distance (ft) (ft)

Hard Soft Hard Soft Hard Soft
0.2 13.2 0.500 0.250 2.36 0.59 0.68 0.17
0.5 20.9 0.500 0.250 3.74 0.93 1.70 0.43
1.0 29.6 0.500 0.250 5.29 1.32 3.40 0.85
2.0 41.8 0.479 0.250 6.87 1.87 6.25 1.70
5.0 66.2 0.371 0.227 6.51 2.43 9.36 3.49
10. 93.6 0.287 0.156 5.50 1.63 11.19 3.31
20. 132.3 0.202 0.085 3.85 0.68 11.08 1.96
25. 147.9 0.174 0.062 3.21 0.40 10.33 1.30
30. 162.0 0.152 0.043 2.67 0.21 9.40 0.76
40. 187.1 0.116 0.013 181 0.02 7.35 0.10
50. 209.2 0.089 0.000 1.18 0.00 5.35 0.00
60. 229.2 0.066 0.000 0.72 0.00 3.57 0.00
80. 264.6 0.030 0.000 0.18 0.00 1.01 0.00
100. 295.9 0.003 0.000 0.00 0.00 0.01 0.00

April 13, 1995 19


Contract No. FO4703-91-C-0112

RTI Report No. RTI/5180/60-31F
Task No. 10/94-60

April 13, 1995

Casualty Areas from Impacting Inert Debris
for People in the Open

Final Report

Prepared by

Robert M. Montgomery
James A. Ward, Jr.

of

Research Triangle Institute
Center For Aerospace Technology
Launch Systems Safety Department

Prepared for

Department of the Air Force
45th Space Wing (AFSPC)
Directorate of Safety - 45 SW/SE
Patrick AFB, FL 32925

and

Department of the Air Force
30th Space Wing (AFSPC)
Directorate of Safety - 30 SW/SE
Vandenberg AFB, CA 93437

Distribution authorized to US Government agencies and their contractors to protect administrative/
operational use data, 13 April 95. Other requests for this document shall be referred to the 30th Space

Wing (AFSPC) Directorate of Safety (0 SW/SE), Vandenberg AFB, CA 93437, or 45th Space Wing
(AFSPC) Directorate of Safety (45 SW/SE), Patrick AFB, FL 32925.



where kinetic energy is converted into pounds of TNT using the standard energy release
for TNT of 10° calories per ton or 1.54 ft-Ib/pound of TNT. This proportionality can be
written in equation form as

kx KE/A (3)

Wi, (lb) = ——
TT 1.54 x 10°

where, without loss of generality, the area A will be chosen in square feet, so the
proportionality constant k, which has yet to be established, will also be in square feet.
Ideally k — which may not be a constant at all but rather some function of w, v, and A
— should be evaluated from experimental data.

Equation (51) and an energy transfer similar to that represented by Eq. (53) appeared in
an earlier RTI working paper'!. No claim was made then or has ever been made by
RTI that the two types of energy will produce the same splatter effects. Rather, since
explosions are considered to be more effective in projecting fragments and crater ejecta
than equivalent-energy impacts, the use of Eqs. (53) and (51) with a suitable value of k
should provide a conservative upper limit for the maximum hazardous distance to
which debris can be splattered by inert impacts.

Since no experimental data were available for evaluating k in Eg. (53), a subjective
procedure was used. To this end, values of r,,,. were calculated from Eqs. (53) and (51)
for several impacting bodies using arbitrarily assigned values of k. Body characteristics
are given in Table 10 and results in Table 11. From an inspection of these results, a
value of k must be chosen.

Table 10. Component Characteristics

Terminal

Item | Atlas IAS Weight | w/C,A | Area | Velocity KE/A

No. | Component (Ibs) (lb/ft?) | (f?) (ft/sec) | (ft-lb/ft?)

1 Turbo-pump 1056 190 7.94 408 3.44 x 10°
assembly

2 Expended Castor 1550 98.8 8.77 294 2.37 x 10°
IVA

3 Centaur engine 442 51.2 13.0 212 2.37 x 10*
assembly

4 Interstage adapter 1206 10.3 72.0 94.9 | 2.34 x 10°
Jettison rail 33 6.6 4.78 76.0 | 6.20 x 107

Aptil 13, 1995 43


Oo q 1/2

Rebound Angle @

Figure 8, Rebound-Angle Density Function for
Intermediate Impact Angle

For the assumed density function in Fig. 8, the slope of the line f,() from A to Dis 8/1’,
while the slope of £,() from D to B is -8/n’. Knowing that the area under the
density-function curve must be unity, with some algebraic manipulation the following
results can be obtained:

2 8
2 fe [Ea] +f 26

B=
(28)
Tt
p-b+ ‘
fis
and.
8
FO) = D + T(o - 4
= ) (29)
@) =D - 2 (o -
i) = (9 - 4)

April 13, 1995 27


The time to reach a height of h, can be computed from Eq. (39) only if the trajectory
rises to or above that height. When the apogee is less than h,, the term under the square
root sign in Eq. (39) is negative, Eq. (40) is bypassed, and d, is set equal to 1,/2.

To carry out the calculations indicated in Eqs. (38) through (40), a value of y is needed.
Rather than select an arbitrary value for y, the following procedure is used to compute
d, for each interval i of width w:

(1) For the maximum hazardous projection range r,., a projection velocity Vinax
is computed from Eq. (38) with y = 45°.

(2) A value of r, is determined from Eq. (35).

(3) | The minimum projection velocity Vai, to reach range r, is computed from
Eq. (38) with y = 45°.

(4) The velocity interval from Vyyin 0 Vmax is divided into m equal sub-intervals.
For each of the m+1 velocities v, the two initial path angles that produce
impact range r, are computed from Egs. (41) and (42), where Eq. (41) is
obtained by solving Eq. (38) for ‘y.

(smaller) = re (| G = 1,2,-,m+1) (41)
J 2 v2
J

y(arger) = 90 - (smaller) @ = 1,2,-,m+1) (42)

(5) For each of the (m + 1) velocities and corresponding pairs of path angles,
values of d; are computed using Eqs. (39) and (40).

(6) Assuming that all velocities and their corresponding pairs of path angles are
equally likely, a mean value of d; is computed from the set of (2m + 1) values
determined in step (5).

Steps (2) through (6) are repeated for all values of i.

After a mean value of d, has been computed for the midpoint of each range interval,
Eq. (37) can be adjusted to eliminate the portion of the ground area swept out while the
fragment altitude is above h, feet. This becomes a little messy because the horizontal
distance traveled while the fragment is below h, must be reduced by the radius of a
person r,. This avoids duplication of the casualty area that has already been included
in the basic casualty area of the impacting fragment [see Fig. 2 and Eq. (4)]. The
adjustment to Egs. (37) is done by replacing (r,-1,) by a quantity Q, which is the
horizontal distance traveled by the projected fragment when it is simultaneously farther

April 13, 1995 36


d=tv (21)

where v,, is determined from the second of Egs. (9).

For this case (high and long bounce), the casualty area due to bounce becomes

A, (bounce) = bef, + r,)a| + Let, + r,)d + nr, + “J | (22)

= 4d(r, + x) + nr, + ry

As in the case of slide, the area of the fragment at first impact must not be included in
Eg. (22), since this area has already been accounted for in the basic casualty area given
by Eq. (4). Since, in fact, the first bracketed term in Eq. (22) does include half the area
of the fragment at impact, the leading half of the fragment at height h, on the way up
is omitted from the equation to compensate for this.

7.7.2 High and Short Bounce

If the bounce distance is not so large, the up and down positions of the bouncing piece
at height h, may overlap. In this case,

d, < 2(a +1, + x) (23)

and elimination of the duplicated area becomes a bit messy. Consider Fig. 6 where the
solid-line circles indicate the positions of the augmented fragment during the first
bounce at height h, on the way up and again at h, on the way down. The distance
between these two positions is (d, - 2d), where d, and d are as defined previously for
Fig. 5.

April 13, 1995 22


person
piece
-

at impact

boundary of
effective casualty area

Figure 2. Casualty Area for Piece Falling Diagonally

Throughout the last h, feet of fall, the motion is assumed to be translational with the
piece oriented so that its largest cross-section is parallel to the ground. The horizontal
distance between centers of the two positions is seen to be

d= h (3)
tany

where d is the horizontal distance traveled by the piece in falling from height h, and
vis the average path angle of the velocity vector relative to the horizontal during the fall.

Circles of radius r, representing a person have been circumscribed about the outer
boundary swept out by the falling piece. Assuming no perturbations upon impact, the
area inside the curve drawn through the centers of the bounding circles represents the
effective casualty area, since any person whose geometric center lies inside this area is
hit, and any person whose center is outside is not.

The effective casualty area due to wind and path angle effects is seen to be

A, (impact angle) = 2(r, + 1,)d + mr, + ry (4)

April 13, 1995 6


Table A4. Atlas IIAS Effective Casualty Areas for Soft-Surface Impacts

Avasic Agiae Asounce Agpiat Age Ratio
Class a) (fe) ) G3) (FE) | Avi/Ataic
Al 23.04 12.10 541 0 35.14 15
A2 48.22 19.14 9.06 0 67.36 14
A3 2641 13.56 7.38 0 39.97 15
A4 41.84 18.20 11.96 0 60.04 14
AS 19.08 11.52 8.36 0 30.60 1.6
A6 7.73 6.68 5.81 0 14.42 19
AZ 49.29 20.72 21.91 “0 71.21 14
A8 9.91 8.60 13.64 0 23.55 24
AQ 8.50 7.89 12.55 0 21.06 25
A10 23.23 14.15 22.57 0 45.80 2.0
All 11.45 9.82 15.14 0 26.59 23
Al2 100.38 31.82 47.65 0 148.03 15
A13 7.90 8.04 11.84 0 19.74 2.5
Al4 38.19 0 26.08 0 64.27 17
A15 9.91 0 10.03 0 19.94 2.0
Al6 6.79 0 4.45 0 11.24 17
A17 5.03 0 3.67 0.35 8.70 L7
A18 11.46 0 4.62 0 16.08 14
A19 60.66 0 3.14 9.00 69.66 1
A20 13.32 0 0.10 4.02 17.34 13
A21 24.60 0 0 11.28 35.87 15
A22 441 0 0 2.56 6.97 1.6
A23 6.54 0 0 9.88 16.41 2.5
A24 21.95 0 0 94.36 | 116.31 53
Pl 35.54 15.95 7.55 0 51.48 14
P2 34.20 17.40 27.39 0 61.59 18
P3 5741 0 29.06 0 86.47 15
P4 14.24 0 13.73 0 27.96 2.0
P5 52.07 0 0 123.96 176.03 3.4
cl 17.99 11.36 9.83 0 29.35 1.6
C2 14.53 10.77 17.09 0 31.62 2.2
C3 21.15 13.70 21.72 0 42.87 2.0
C4 6.25 0 3.34 0 9.60 15
C5 10.00 0 0 5.26 15.26 15
C6 * 5.81 0 0 15.41 21.32 3.6
c7* 6.45 0 0 27.32 33.87 5.2
c8* 148.94 0 0 216.27 | 365.02 2.5
co* 148.59 0 0 377.35 | 525.84 35
C10 * 148.99 0 0 202.27 | 351.06 2.4
cl* 148.60 0 0 372.31 520.81 35

* Data for these classes taken at 20 seconds

April 13, 1995

58



Table 11. Maximum Splatter Range (Tax)

Max Splatter Range (ft) for Items in Table 7
k (ft) 1 2 3 4 5
1.0 475 42.1 20.1 9.5 6.2
08 44.2 39.2 18.7 8.9 5.8
0.6 40.3 35.8 17.0 8.1 5.3
0.4 35.4 31.4 15.0 . 7A 46
0.2 28.3 25.1 12.0 5.7 3.7
0.1 22.6 20.1 96 AS 3.0

Although perhaps trivial, Eq. (53) can be applied to TNT if the kinetic energy released
by an explosion is assumed to occur over an area of one square foot and the constant
k is set equal to one. Since intuition suggests that TNT should be more effective in
propelling pieces than an equivalent-energy impact, it seems logical to use a value of k
less than one in calculating maximum splatter range. Due to the lack of experimental
data, subjective considerations cannot be avoided in choosing a value. For example, just
how close would a person located on a hard surface willingly stand to a 1056-pound
turbopump assembly (Item No. 1) that impacts at 408 ft/sec? Practical experience fails
because impacts witnessed in life are, for the most part, at much lower velocities.
Although intuition is not necessarily a good guide, RTI has answered the turbopump-
distance question raised above by choosing k = 0.6 ft”. Since there seemed to be no good
reason for doing otherwise, a value of k = 0.6 was chosen for all other impacting inert
components as well.

For pieces resulting from vehicle breakup, a kinetic-energy threshold has been implicitly
established by assuming that the splatter area is zero unless r,,,,(splatter) exceeds
3.1 feet. Below this threshold, hazardous splattering will not occur. Instead, the
impacting piece may slide or skid, or may deform and bounce without breaking apart.
Applying Eq. (51) with r,,,.(explosion) = 3.1 feet and converting pounds of TNT into
ft-lbs of energy using Eq. (53) with k= 0.6, the threshold for splatter becomes
approximately 120 ft-Ibs/ft?. This kinetic energy is achieved by a one-square-foot body
having a ballistic coefficient and weight per unit area of 3 Ibs/ft* and a terminal velocity
of 51 ft/sec.

8.7 Number and Weight of Splatter Fragments

Having established procedures for estimating the effective splatter area if N pieces are
projected from an impacting component or fragment, a numerical value must be derived

April 13, 1995 44


redrawn to pass more closely to plotted data points or extrapolated to zero percent.
Percentages read from the remaining four curves, as modified, are given in Table 13.

Table 13. Percent of Total Weight of Fragments Within Indicated Range

Range (ft) | Atlas Centaur | S-IVB-ASTV | S-IV-EAFB | S-IVB-503

1000 - - 101 98
900 - 97.5 100 94
800 - 97.5 97 90
700 - 97 . 91 88
600 - 96.5 82.5 86
500 101 93 71 80
400 99 80 55 66
300 94 49 49 50
200 82 18 17 31
100 Al 4 0 11
50 0 0 - 0

The data in Tables 12 and 13 will now be used to estimate the total kinetic energy
imparted to vehicle fragments by their respective explosions. By differencing
percentages in Table 13 and multiplying by the total fragment weight given in Table 12,
the weight of fragments impacting in each range interval can be found. If a ballistic
coefficient and initial path angle are assumed, the projection velocity needed to produce
impact at the midpoint of each range interval can be calculated. With fragment weight
and velocity determined for each range interval, the KE can be calculated and then
summed for all intervals. This energy can be converted into equivalent pounds of TNT,
then divided by the yield in Table 12 to provide an estimate of the percent of explosive
energy that is effective in propelling fragments away from the explosion.

Since the effective ballistic coefficient (B) of the fragments and initial projection angles (y)
were unknown, computations were made for several values of each parameter. Results
are given in Tables 14 and 15 for the S-IVB-EAFB accident at Edwards Air Force Base,
where the foot-pounds of kinetic energy shown in Table 14 have been converted into
equivalent pounds of TNT in Table 15. For smaller values of B, the velocity needed to
reach the midrange of the longer range intervals was several thousand feet per second.
According to CPIA Publication 394 (Vol. 1, September 1984), Baker"?! established from
Project Pyro data and explosions of other liquid-propellant motors that the mean initial
fragment velocity from liquid-propellant explosions could be represented by the equation

v = 74 Ws 4)

April 13, 1995 46


Table 3. Horizontal Slide Distance

Initial Horizontal Slide Distance (ft)
Horizontal
Speed (ft/sec) £=0.3 f£=04 f=0.5 £=0.6 f=0.7 | f=08

5 13 1.0 0.8 0.6 0.6 0.5
10 5.2 3.9 3.1 2.6 2.2 19
15 11.7 8.7 7.0 5.8 5.0 44
20 20.7 15.5 124 10.4 8.9 78
25 32.4 24.3 19.4 , 16.2 13.9 12.1

Although in theory the computation of slide distance is straightforward, major
uncertainties arise in applying the procedures to impacting vehicle fragments or
components:

(a) Immediately after impact, there is no suitable way to estimate the residual
horizontal velocity of a sliding fragment;

(b) The impacted surface may be irregular and non-homogeneous, so the
deceleration during the stopping period may vary considerably;

(c) The coefficient of friction between a deformed body and an unknown surface
cannot be accurately estimated, and surely is not constant;

(d) While coming to rest, a body that is primarily sliding may also roll, bounce,
tumble, or dig into the surface.

Since a soft surface is more likely to be irregular than a hard surface, and since an
impacting body is more likely to dig into a soft surface as it slides or tumbles along, it
seems reasonable to assume that the coefficient of friction, on average, is higher for soft
surfaces. At some impact velocity, slide is unlikely to occur either because the impacting
body digs into a soft surface, or bounces or shatters following a hard-surface impact.
The no-slide velocity varies widely depending primarily on the composition of the
impacting body and its attitude at impact. Although no real justification exists, a
constant no-slide threshold for the vertical velocity component has been chosen, since
there seems to be little point in postulating some artificial density function for the
threshold.

6.3 Assumptions
Although all of the above factors contribute to the uncertainty of the result, quasi slide

cannot be discarded as an impossibility, particularly early in flight or for low-velocity
fragments that impact at any time on hard surfaces such as concrete, blacktop, packed

April 13, 1995 9