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TECHNICAL REPORT ARBRL-TR-02234
TERMINAL EFFECTIVENESS, VULNERABILITY
METHODOLOGY AND FRAGMENTATION
WARHEAD OPTIMIZATION. I. A TECHNICAL
SURVEY FROM AN HISTORICAL
PERSPECTIVE ^-,
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James T. Dehn /
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April 1980 --:.;: r :. ~ ^
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US ARMY ARMAMENT RESEARCH AND DEVELOPMENT COMMAND
BALLISTIC RESEARCH LABORATORY
ABERDEEN PROVING GROUND, MARYLAND
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TECHNICAL REPORT ARBRL-TR-02234
4. TITLE (andsUbtiti.) TERMINAL EFFECTIVENESS. VULNER-. - 5. TYPE OF REPORT ft PERIOD COVERED
ABILITY METHODOLOGY AND FRAGMENTATION WARHEAD
Final
OPTIMIZATION. I. A TECHNICAL SURVEY FROM AN
HISTORICAL PERSPECTIVE 6. PERFORMING ORG. REPORT NUMBER
7. AUTHORfej 8. CONTRACT OR GRANT NUMBER(s)
James T. Dehn
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Aberdeen Proving Ground, Maryland 21005 1L161102AH43
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Terminal Ballistics
Vulnerability
Fragmentation
Warhead Optimization
20. ABSTRACT fCtttrtfaua an renr*» eMf tt nexfeeezr antt Identify by block number) (Jj;j_|O The design Of 3
fragmentation warhead for optimal effectiveness requires a knowledge of frag-
ment formation, launch and flight characteristics as well as penetration ability
and target vulnerability. In addition, a knowledge of the expected engagement
conditions between warhead and target as well as weight, volume and other design
constraints is needed. Present views of the subject have developed over more
than forty years, so it is to be expected that an intimate knowledge of this
development will prove to be helpful in making further progress. For this
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TABLE OF CONTENTS
Page
I. INTRODUCTION
7
II. EFFECTIVENESS STUDIES UNTIL THE END OF WWII
g
A. Methodology Prior to WWII (Kent and Tolch). . . .. 8
B. The Variable Time Proximity Fuse
(OSRD 738, Kendall, Mott, Morse, Chandrasekhar and
Lewy) 20
C. Further Developments. Two Kinds, of "Lethal Area"
(Thomas, Gurney, Lewy, Morse, Scheffe', Pearson
and Carlton) 37
III. EFFECTIVENESS STUDIES AFTER WWII 50
A. The Refinement of Analytical Methods. The Adoption
of Numerical Integration for Ground Effectiveness
Problems. (Weiss and co-workers, Allen and
Sperrazza, Myers) 50
B. The Adoption of Monte Carlo Methods for Air Defense
Problems (King and co-workers, Monks) 62
C. Current Vulnerability Methodology. Warhead Optimi-
zation. (Mowrer and Go-Workers, Dougherty, Sewell,
Scherich and Kitchen),' 65
IV. CONCLUSION 74
APPENDIX I. Some Early Workers in the Field 75
APPENDIX II. Fragment Presentation Area and Shape
Factor 77
REFERENCES. 83
DISTRIBUTION LIST 91
This page Left Intentionally Blank
LIST OF ILLUSTRATIONS
Figure Page
1. Fall-off in Effectiveness Subdivided According
to Fragment Weights (from OSRD 738) 23
2. Geometry of a Burst over the Ground Plane (from
BRL R530). 45
3. Typical Kill Probability versus Striking Speed Curve for
a Given Fragment Mass and Kill Criterion (from BRL
R1789) 67
This page Left Intentionally Blank
I. INTRODUCTION
Kinetic energy projectiles and shaped charge jet warheads require
direct hits to inflict target damage. A warhead carrying a self-forg-
ing fragment need not hit the target, but its orientation and fuzing
must be exactly controlled for its lethal mechanism to hit the target.
When direct hits by the warhead are unlikely (as in long range engage-
ments or for partially concealed targets) or not required (as in the
case of a collection of widely distributed targets) fragmentation
warheads are employed. Since direct hits are not contemplated, the
flight and fuzing requirements of such warheads are less stringent.
However, the design of the warhead itself requires great care if its
effect on the target is to be nearly optimum. The best design for a
fragmentation warhead obviously depends on a knowledge of target
vulnerability as well as on the engagement conditions and the various
options that are available regarding fragment number, size and launch
characteristics. The problem of designing such a warhead for optimum
effect is rather complicated and is made more difficult by the uncer-
tainty of our knowledge about target vulnerability and fragment
characteristics. If each warhead is required to address more than
one type of target (as is often the case), the problem is still more
difficult. In spite of these difficulties, the problem of optimizing
or at least of estimating the effectiveness of a design has received
considerable attention over the last half century. However, for a
variety of reasons, the trend has been toward the inclusion of more
and more detail in model descriptions of effectiveness and away from
design optimization.
In current design practice for fragmentation warheads, the focus
is usually on the delivery system. Of course, this system is impor-
tant and inevitably places weight and/or volume constraints on the
warhead designer. However, there is a tendency to incorporate tradi-
tional warhead designs into new delivery systems, with warhead effec-
tiveness studies performed only after the overall design has been fixed.
This tendency is understandable but regrettable. It seems obvious
that the goal of optimal warhead effectiveness should drive the overall
design of a system, especially when direct hits are not contemplated.
The warhead designer should in fact propose configurations of metal
and explosive armed at maximizing target kill probability even if
they tax the ingenuity of his colleagues to deliver them to the target.
In this way significant improvements might result from compromises
between an optimum warhead and an optimum delivery system. However,
our methods of describing warhead effectiveness need to be simplified
first before attention can be re-directed toward those factors which
most influence effectiveness. The eventual object of this report
series is to employ simplified descriptions as an aid to design
optimization. The object of this report is to review the development
of our present methods as a prelude to suggesting improvements.
II. EFFECTIVENESS STUDIES UNTIL THE END OF WWII
A. Methodology Prior to WWII
There seems to be little extant literature on this subject written
prior to the second world war. Of course, devices which explosively
launched pieces of metal were in use, but early treatises on ballistics
emphasized launch and flight techniques. Relatively little attention
was paid to measures of effectiveness, either absolute or relative.
This was reflected in the organizational structure of the Ballistics
Research Laboratory when it was established in 1938. There were
Interior and Exterior Ballistics Sections, but no Terminal Ballistics
Section until 1943. Instead, a small Effect of Fire Unit within the
Interior Ballistics Section conducted fragmentation and penetration
studies. Eventually the Terminal Ballistics Section was entitled a
Laboratory and gave birth to the Vulnerability/Lethality Division.
The need for an overview of all aspects of cost/effectiveness led to
the establishment of a Weapons Systems Laboratory within BRL and
eventually to the Army Materiel Systems Analysis Activity1.
The earliest paper on the subject of fragmentation effectiveness
appears to be Kent's report in 19332. Kent .took as a measure of
effectiveness the number of casualties produced (personnel put out
of action). He commented on the desirability of measuring effectiveness
by the extent of damage produced, especially for materiel targets like
aircraft where the number of man-hours needed to repair the damage
might be a useful criterion. However, for footsoldiers he choose a
simple threshold criterion to distinguish between a casualty and a
survivor. He directed his attention to the simple case of a vertical
cylindrical shell bursting at ground level in an effectively infinite
field of uniformly distributed, unshielded, standing personnel targets.
He wrote an expression for the.number of casualties, C, namely,
00
C = T ir r^ T f N (A /r2) (2* rdr) (i)
A A fi p
rl
where T is the constant number of targets per unit area of ground.
2
The radius, r.., defines an area (irr.J on the ground, centered at the
burst point, within which a target will receive at least one lethal hit.
All targets in this area will be casualties, but there is a loss in
efficiency since multiple lethal hits are wasteful. Consequently,
the distance r was called the radius of overhitting.
^•Ballisticians in War and Peaoe. A History of the United States
Army Ballistic Research Laboratories, Vol. I 1914-1956 , Edited
3
by John Schmidt, Aberdeen Proving Ground; MD pp 12 21 47 and 98-102.
3 3 3
2R. H. Kent "Considerations on the Effect of the Size of the Projectile
3
on the Efficiency of its Fragmentation", BRL RX-58 Feb 1933.
3
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