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Determining The Relative Detectability
Of Ground Weapon Systems
CSC 1984
SUBJECT AREA Operations
                    DETERMINING THE RELATIVE DETECTABILITY
                                      OF
                             GROUND WEAPON SYSTEMS
                                 SUBMITTED TO
                  THE MARINE CORPS COMMAND AND STAFF COLLEGE
                              QUANTICO, VIRGINIA
                    IN PARTIAL FULFILLMENT OF REQUIREMENTS
                          FOR WRITTEN COMMUNICATIONS
                            MAJOR EDWIN T. CARLSON
                              UNITED STATES ARMY
                                APRIL 20, 1984
Introduction
     There is a common maxim of ground combat which states, "If you can see a
target, you can hit it."  The validity of this assertion is apparent since
today's direct fire weapons are characterized by such high velocity trajector-
ies that the projectile almost follows a line of sight from the weapon to the,
target in a matter of seconds or fractions of seconds.  To take full advantage
of these weapons improved sighting systems, night optics, and laser range
finders have been developed by both western and Warsaw Pact countries.  These
sighting devices are designed to improve target detection capabilities and to
speed target engagements.  Such advances in weapons technology have precipi-
tated serious concerns about the survivability of ground weapon systems on
future battlefields.  Lower silhouettes, faster speeds and less exposure times
during engagements are becoming primary weapon system design characteristics.
     An individual gunner or crew depends on his or their weapons to defeat
the target, to operate reliably and safely, and to be employed with minimum
exposure to enemy observation and fire.  This latter attribute of the weapon
is often the most difficult characteristic to determine objectively.  It is
relatively easy to conduct a test to confidently determine a weapon's
accuracy and lethality against prospective targets.  It is also relatively
easy to confidently assess the weapon's reliability under different conditions
and rates of fire.  Operational weapons testing can provide the results of
accuracy and reliability testing but usually provide only subjective esti-
mates of a weapen's susceptability to detection by the enemy.
     The operational user of the weapon to be procured, the Army or Marine
Corps, usually ask the correct questions about the survivability of a new
ground weapons system.  However, operational and developmental testing has
usually only been sufficient to provide subjective answers where objective
answers would be better.  Objective answers provide the best means for fully
informed procurement decisions.  The focus of this paper is to establish a
method of operational testing and analysis of ground anti-tank weapons
systems that will provide an objective assessment of firing signature detecta-
bility.
Theory
	A ground weapon system is (the) most vulnerable to detection when it fires.
The associated smoke, flash, and noise signals all who may be observing the
battlefield disclosing the weapon's presence and location.  The magnitude of
this disclosure (the amount of smoke and flash, and the loudness), the speed
with which it can be detected and engaged, and the accuracy of the enemy to
pinpoint its location are the keys to objectively determining the detectabil-
ity of amy ground weapon system.  The parameters of interest to the analyst
and ultimately to the decision maker would be the probability of detection,
the times to detect and engage, and the accuracy with which the weapon position
was pinpointed.
	The probability of detection of a weapon system as it fires can be esti-
mated in operational testing by requiring independent observers to survey a
simulated battlefield and record the number of times they detect a firing
weapon.  As the number of observers are increased and the weapons are fired
under varying conditions such as light (day/night) and range (distance from
firing location to observers), the frequency of detection provides a good
estimate of the probability of detection; 
p = (# detections) / (# firing) x # observers. (THIS REPRESENTS DIVISON)  In
probability theory this function is the maximum likelihood estimator for a
random variable taken from a Binomial distribution.  The Binomial distribution
best models the actual process of a string of detection opportunities which is
of the form 0 or 1 or Yes/No.  That is, only one of two possible outcomes will
occur in any trial.  This is much like the toss of a coin, heads or tails.
Ultimately the actual probability of occurrence associated with such a Binomi-
al distribution will be  p (heads) = # heads/total # of tosses.1(THIS REPRESENTS DIVISON) 
     It is expected that each observer will take a different length of time to
detect the weapon.  For each firing of a weapon the time begins when the
weapon fires and is precisely stopped when an observer thinks he detects the
weapon.  The collection of these times for each weapon and for each observer
provide a distribution of time increments.  If all of these time increments
are plotted in a cumulative distribution function the function will resemble
that in Figure 1.
Click here to view image
     This cumulative distribution function is of the exponential form
F(t) = 1-e-Kt.2  One hundred percent of all firings would rarely all be detec-
ted by all observers so the function only approaches the 100% line as a limit
as time goes to infinity.  The time corresponding to the 50% point on the
curve is called the median time and is the time above and below which 50% of
all detections occurred.  The median is considered a better measure of central
tendency of the time distribution as opposed to the mean or average time.
Some observers never detect some weapons and their detection times on these
opportunities are running into infinite time.  Including these trials in the
average would skew the mean and omitting them would be less representative of
what actually occurred.  Therefore, the median detection time will be used as
the parameter that best represents the expected time for a detection to occur.
     The accuracy with which an observer can locate or pinpoint the weapon due
to its firing signature can be measured if both the weapon and observer loca-
tions are precisely known and the observer can provide an azimuth and range
estimation from his position to the target.  By plotting weapon and observer
locations, observer azimuth, and range estimation on a map the lateral error
can be determined for each trial.  Figure 2 depicts how this would look.
Click here to view image
	The observer error is measured from the actual firing weapon location to
the point determined by the observer's azimuth and range estimation.  For
better accuracy the positions of the observer and the firing weapon should be
surveyed to at least eight-digit grid coordinates, providing an accuracy of
plus or minus 10 meters.  Ten-digit grid coordinates provide an accuracy of
plus or minus one meter.
     The collection of these lateral observer errors form a distribution from
which certain summary statistics such as the mean and standard deviation can
be determined.  The mean of this distribution is simply the average distance,
expressed in meters, between the actual weapon location and the estimated
weapon location.  The relative magnitude of this average error objectively
determines the accuracy with which observers could pinpoint the weapon's
location based upon detection of its firing signature.
Previous Testing
     Research reveals that only two opetational tests have been conducted in
which the above method or variations of these methods have been used.  In 1955
Project Pinpoint was conducted to provide information related to the problem
of target acquisition by tanks in an overwatching role and to determine the
effects of several factors on target acquisition, such as weapon type, light
condition and range.3 In 1981 the Viper Light Antitank Assault weapon was
tested during its Operational Test II (OT II) to determine its detectability
relative to the M72 LAW, which the Viper was designed to replace.4
	The unknown variables in each test consisted of the frequency of detec-
tion, the time to detect and engage, and the accuracy with which the observers
could pinpoint the firing weapon.  The controlled variables common to both
tests consisted of the type weapon, the range between observer and firing
weapon, and the light condition (day or night).  Project Pinpoint also varied
the number of times the same weapon fired from the same location to determine
the effect of multiple firings on target acquisition and detectability.  Due
to ammunition constraints the Viper and LAW only fired once from each position
per trial.  Whereas the Viper OT II tested the comparative detectability of
the Viper and the LAW, Project Pinpoint tested the battalion antitank (BAT)
rifle, the M48 90mm tank gun, and the 76mm towed antitank gun.
     Data collection requirements for both tests included the number of detec-
tions, the time to detect and engage, the precise location of observers and
firing sites, the azimuth determined by the observer from his position to
where he thought the firing weapon to be, the observer's range estimate to the
target, and the particular component of the firing signature which prompted
detection of the firing weapon.
     Observers in both tests were mounted in tanks.  Several reasons contrib-
ute to this being an excellent consideration.  First, the safety of the
observers, even though they were outside the firing fans of the weapons, was
enhanced.  Second, observation of the battlefield by overwatching tanks was
realistic.  Third, the tank's fire control system and azimuth indicator mounted
on the turret ring provided an excellent means of measuring the azimuth from
the tank to the detected target.  They also accurately measured the speed of
engagement as the crew went through the drill of ranging, loading and
simulated firing at the target.  Fourth, the range finder of the tank gave the
observer the means to determine more accurately the range from his position to
where he thought the target was.
     The simplicity of this method of collecting data on ground weapon system
detectability is appealling.  There are no unique test site requirements other
than those of a range facility appropriate to the size of the weapon being
tested, a downrange observer tank area which provides visibility of the firing
sites, and the ability to survey weapon and tank locations precisely.  The
observers need no other qualifications other than those expected in any compe-
tent tank crew   The primary observer would, naturally, be the tank commander
for each tank.  The gunners or crews of the ground weapons being tested would
require training on that weapon, but no additional training, beyond sound
employment techniques, would be needed for them to participate in such a
detectability test as discussed here.  The data collectors have to be capable
of keeping the same time accurately at the firing site and at each observer
tank.  Questionnaires have to be issued to each tank commander to determine
the particular firing signature component that cued his detection of the
target.  Multiple firing sites must be surveyed to prevent the observers from
limiting their visual search area to the particular sites they may begin to
learn as the test is conducted.  The test must be conducted under operational
conditions.  The more artificiality induced in the conduct of the test will
make the validity of results more questionable.
     Once the test is completed and the data is validated, correct data analy-
sis will allow the operational evaluator to begin to objectively answer cer-
tain key questions prompted by the concerns of the operational user.  These
are:
          .    What is the frequency of detection?
          .    Which signature components are the most significant?
          .    How quickly can the weapon be detected and engaged?
          .    How accurately can the weapon's location be pinpointed?
Methods of data analysis to provide answers to these questions are
below using examples from the Viper OT II and Project Pinpoint.
Frequency of Detection
     As discussed earlier, the frequency of detection is merely the total
number of detections divided by the total number of detection opportunities
and can be written as a percentage.  Table 1 and Table 2 present the parcent-
age of detection for Viper and LAW overall and differentiated by light condi-
tion.5  The numbers in parenthesis are the number of detection opportunities
that occurred in the test for any set of weapon and light conditions.  In the
Viper OT II thirty-two rounds of Viper and LAW were fired.  Five observer
tanks afforded the opportunity to attain a possible 160 detection events for
each weapon system.  However, a sample population of only 155 detection oppor-
tunities for Viper and 158 for LAW were considered for analysis, since seven
unresolved data base errors prevented all 320 data elements from being used.6
Click here to view image
     Overall the Viper was detected 73.5%  (114/115 = .735 X 100 = 73.5%) and the
LAW was detected 42.4% of the time.  The Chi-Square test of a difference of
two proportions was used to confirm statistically that the difference between
these two results is significant.7
Signature Component
     In the Viper OT II the observers were questioned concerning the particu-
lar component of a launch signature that was responsible or partly responsible
for detection of the system.  These data are presented in Table 3.  As can be
seen, the majority of detections of both systems were due to flash, smoke and
the combination of flash and smoke.8
     The correlating of signature components and frequency of detection as is
done in Table 3 provides the analyst with not only the means to determine
which signature components were significant, but also the means to statisti-
cally determine to what degree each component or combination of components
contributed to detection.
Click here to view image
Time to Detect and Engage
     Given that the observers in the tanks observed a weapon fire, the time to
detect is determined on a time-line that includes exact time of firing and
exact time of detection.  The time to detect a given firing can then be deter-
med as the magnitude, in seconds, of the interval between the two times.  As
an example, the cumulative distributions for both Viper and LAW detection
times are presented in Figure 3.9  For such distributions the median time is
preferred as the measure of central tendency, as mentioned earlier.  Interest-
ingly, in the Viper OT II the Viper and LAW detection time distributions  were
essentially the same and were found not to be significantly different.  The
median time to detect both LAW and Viper was found to be the same at 3 seconds.10
Click here to view image
	The time to engage the detected system was also determined on the same
time-line so that the time to detect the system and the time for the tank crew
to return fire with the main gun could be determined.  Figure 4 presents the
time to detect and return fire (counter fire time) on both LAW and Viper
systems.11  As seen, the distribution of times for both systems is very simi-
lar with a common median time to detect and return fire of 9 seconds.  In
Viper OT II neither LAW nor Viper were faster to detect and to simulate engage-
ment by the observer tanks.
     Analysis of the Project Pinpoint recognition time data (equivalent to the
counterfire time variable of Viper OT II) reveals the same phenomenon.  The
cumulative frequency distributions of detection times for the BAT, the tank,
and the towed gun (see Figure 5) were found not to differ significantly with a
median time of 8 seconds.
     It would be premature at this writing based on the results of Viper OT II
and Project Pinpoint to suggest that the time to detect a ground antitank
weapon system is independent of the type weappon.  However, future evaluators
should not be surprised to discover similar results in such tests of newer
weapons.
Click here to view image
Pinpoint Accuracy
     The expression, lay of the gun, denotes the action of a tank crew bring-
ing their main gun to bear on a prospective target, ranging to the target and
selecting the appropriate ammunition.  Laying the gun essentially equivocates
to those tasks necessary for target engagement.  The azimuth indicator, mount-
ed on the turret ring, can be zeroed at an arbitrary point of reference and
all azimuths of gun lay can be measured with respect to this point of refer-
ence.  This method was used in the Viper OT II and Project Pinpoint.  The
azimuth from the lay of the gun to the target area was compared to the true
azimuth from each tank gun to the actual weapon position, which were accurate-
ly surveyed for this very purpose.  This angular difference, measured in mils,
was converted to meters at the true range of the target system in order to
determine the distance right or left of the true location at which a fired
tank projectile would pass or impact (1 mil equates to 1 meter at 1,000
meters).  Figure 6 graphically depicts the method of determining the ob-
server's horizontal error.
Click here to view image
  Figure 6.  The technique of determining an observer's horizontal error.
The distribution of all horizontal lay errors then can be analyzed to deter-
mine certain summary statistics such as mean, median and standard deviation.
Figure 7 presents cumulative frequency distribution of the horizontal errors
for Viper and LAW.14  The average horizontal error obtained against the Viper
was 22.7 meters and against the LAW was 23.9 meters.15  Confidence intervals
can be constructed using this data at the level of confidence required to
determine if a significant difference in accuracy exists between the two
weapons being compared.
     In Viper OT II the results of this analysis indicate that the Viper was
not significantly easier to locate or engage accurately than the LAW, with
about 60 percent of the pinpoint positions of both systems less than 25 meters
from the true location.16  Project Pinpoint results, shown in Figure 8, were
that the average lay error was about 5 yards for each tested system, with 80
Click here to view image
percent of all errors within the limits of 25 yard lay error.17  As in the
Viper OT II analysis, Project Pinpoint results also saw no affect on pinpoint
accuracy due to the weapon type.
     Another method of evaluating the accuracy with which detected ground
weapon systems can be engaged is to determine the radial error involved in
each engagement.  By plotting the observer range estimation on the observer
azimuth a point of impact can be determined.  The distance from this point of
impact to the true target location is the radial error for that particular
trial (see Figure 2.).  The distributions of these radial errors for each
tested weapon will provide a comparison of the accuracy with which observers
could bring indirect fire, mortars and artillery, to bear on the target.18
Click here to view image
Discussion of Findings
     The methods of analysis discussed above and their results must be evalua-
ted without forgetting the conditions under which the data were collected.
This is why the proper operational setting and weapon employment procedures
must be adhered to during the course of the test.  If the tests were conducted
under realistic operational conditions the evaluator can state his findings
with some confidence that the test results approximate those results which may
be achieved in combat.  Attempting to answer the questions posed earlier, the
Viper OT II and Project Pinpoint results parallel each other as follows:19
          .    The probability that an antitank weapon will be detected was
               dependent on the type of weapon.  Viper was more detectable
               than LAW.
          .    Flash and smoke, and the combination of flash and smoke, were
               responsible for the majority of detections.
          .    If an antitank weapon were detected, the time to detect the
               target was not affected by the type of target weapon, the
               target angle, or the target range.  The time to detect the
               Viper was not significantly different than the time to detect
               the LAW.
          .    The horizontal lay error (pinpoint accuracy) with which a tank
               crew could engage a firing weapon system does not differ
               significantly between different weapon systems provided a
               detection is made.   Eighty percent of all lay errors were less
               than 25 yards right or left of the true target location in
               Project Pinpoint.  The accuracy of pinpointing the LAW or Viper
               system was not significantly different.  Sixty percent of all
               lay errors were found to be less than 25 meters or each system.
Payoff Ratio
     The issue of a weapon system's vulnerability to detection by enemy
observers provides some insight into the broader issue of the survivability of
the weapon and its' gunner or crew.  If a weapon is rarely detected when it
fires, it follows that it has a better chance of survival on the battlefield
than a weapon that is frequently detected.  The point at which the detectabi-
lity of a weapon seriously endangers its survivability cannot be objectively
determined. It is a subjective determination by the operational evaluator and
decision maker.
     An aid to the evaluation of this question is the construction of a payoff
ratio.  The payoff ratio takes into-consideration the fact that a gunner may
be willing to risk a higher probability of detection in order to achieve a
higher probability of hit.  This was the case in the Viper OT II.  The Viper
attained an overall probability of hit, Phv, of 0.51 in the test as compared
to the LAW's probability of hit, PhL, of 0.24.20  As mentioned in the previous
analysis the Viper's overall probability of detection was Pdv = 0.735 as
opposed to the LAW's lower probability of detection PdL = 0.424 (see Table 1).
Though a Viper gunner had a better chance of hitting his target, he also had a
better chance of being detected once he fires.  The overall comparison of
Viper and LAW really amounts to an assessment of the trade-offs between each
weapon's performance accuracy and survivability.  If a ratio of these trade-
offs is written, it could take the following form:
(Phv)(PSv)/(PhL) (PSL) (THIS REPRESENTS DIVISION)
where:
               PhL = probability of hit by LAW
               Phv = probability of hit by Viper
               PSL = probability of survival for LAW gunner
               Psv - probability of survival for Viper gunner
     Gunner survival can be essentially assured if the gunner is not detected
by any observer upon firing, or, if detected by at least one observer, can
reach cover in some time less than the observer can bring counterfire on his
firing position.  Pd is the probability that a gunner is detected by one
observer upon firing, then (1 - Pd) is the probability that he is not detected.
For n observers, the probability that he is not detected by any observer is
(1 - Pd)n, assuming that all observers have the same probability of detection,
Pd.  The counterfire time distribution in Figure 4 is of the form
                             F(t) = 1 - e-k(t-to)
The probability of the observer firing in some time t, greater than the time
the gunner can take cover is
                              1-F(t) = e-k(t-to)
The probability, P, that the gunner will be detected by at least one obser-
ver, when n observers are present is
                              [1 - (1 - Pd)n] = P
(This is the probability of at least one detection from n observers.)  Thus,
the payoff ratio of Viper to LAW can be written as
Click here to view image
where to is the earliest time counterfire can be returned.  Since the counter-
fire time distributions for Viper and LAW in Figure 4 are essentially the same
		k/v = k/L = 1/t-t/0  (THIS REPRESENTS DIVISON)						
     The probability of survival for each weapon appears complicated but is
merely the probability that the LAW or Viper gunner is never detected or, if
detected, can find cover faster than at least one observer can engage him.
Using the data attained in the Viper OT II where the average engagement time
was 9 seconds.
Click here to view image
and n is the number of observers.
     Table 4 presents the values of this payoff ratio for increasing time to
take cover and for one, two and three observers.21  It is evident that the
Viper payoff decreases as the gunner remains exposed longer after firing and
the number of potential observers increase.  If the gunner can reach cover
immediately (3.5 seconds or less), the payoff ratio merely becomes the ratio
of the probilities of hit, since the probabilities of survival are essentially
one.  (It is assumed for simplicity that once a gunner can reach a covered
position, his probability of survival is unity.)  Any payoff ratio value
greater than one indicates that the Viper offers the greater payoff.  Payoff
ratio values less then one indicate that the LAW is the most advantageous
system.
Click here to view image
     The payoff ratio shows that the Viper can offer a viable advantage over
the LAW in spite of its increased detectability.  It is also surmised that the
Viper gunner Would be ill-advised to fire the Viper more than once from the
same position, since the results of Project Pinpoint indicate that the proba-
bility of detection increases with successive rounds fired from the same
position.22
Conclusions
     Operational testing of ground weapons systems can objectively address the
issue of the weapon's detectability in order to provide better answers to the
user's issue of survivability.  The methods of testing, data collection, and
analysis advocated herein present some guidance as to how this may be accom-
lished.  The demands upon the operational tester are minimal.  There is a need
for tank-mounted observers in safe down-range locations, firing sites and tank
sites must be accurately surveyed to ten digit coordinates, and accurate time
keeping capabilities must be present at all locations.  A detectability sub-
test could be easily incorporated into the weapon accuracy portion of the
operational test, and need not be conducted for its own sake.  Of special
importance is the need to retain operational realism in the employment of the
tested weapons and the observer tanks.
     The data attained can be analyzed using the very simple statistical
techniques presented above.  More sophisiticated analysis can be used but are
beyond the scope of this paper.  Determination of a payoff ratio should aid in
providing a good assessment of the trade-offs between accuracy and detectabil-
ity.  In addition to determining the extent of the payoffs for each system
tested, certain insights can be gleaned from this analysis concerning proper
weapon employment techniques that can take full advantage of weapon accuracy
and still reduce weapon detectability to an acceptable level.
                                  REFERENCES                            
1Morris H. DeGroot, Probability and Statistics (Reading:  Addison-Wesley
Publishing Company, 1975), p. 285.
2Leonard Kleinrock, Queuing Systems (New York:  John Wiley and Sons, Inc.,
1975), p. 66.
3John P. Young, Andrew T. Ackles, et. al., Project Pinpoint; Disclosure of
Antitank Weapons to Overwatching Tanks (Chevy Chase:  John Hopkins Uni-
versity, 1958), p. 1.
4U.S. Army Operational Test and Evaluation Agency, Independent Evaluation of
the Viper Light Antitank/Assault Weapon, XM 132, Operational Test II
(Falls Church, 1981), p.6.
5Ibid., p. 29.
6Ibid., p. 28.
7Ibid.
8Ibid., p. 30.
9Ibid., p. 32.
10Ibid., p. 31.
11Ibid., p. 33.
12Ibid., p. 31.
13John P. Young, Andrew T. Ackles, et. al., Project Pinpoint; Disclosure of
Antitank Weapons to Overwatching Tanks (Chevy Chase:  John Hopkins Uni-
versity, 1958), p. 57.
14U. S. Army Operational Test and Evaluation Agency, Independent Evaluation
of the Viper Light Antitank/Assault Weapon, XM 132, Operational Test II
(Falls Church, 1981), p. 34.
15Ibid.
16Ibid., p. 31.
17John P. Young, Andrew T. Ackles, et. al., Project Pinpoint; Disclosure of
Antitank Weapons to Overwatching Tanks (Chevy Chase:  John Hopkins Uni-
versity, 1958), p. 51.
18U.S. Army Operational Test and Evaluation Agency, Independent Evaluation of
the Viper Light Antitank/Assault Weapon, XM 132, Operational Test II
(Falls Church, 1981), p. 35.
19Ibid., pp. 35-36.
20Ibid., p. 39.
21Ibid., p. 40.
22Ibid., p. 39.
                                 BIBLIOGRAPHY
1.   DeGroot, Morris H., Probability and Satistics.  Reading;  Addison-Wesley
     Publishing Company, 1975.
2.   Independent Evaluation of the Viper Light Antitank/Assault Weapon, XM 132,
     Operational Test II.  U. S. Army Operational Test and Evalution Agency,
     1981, IER-)T-279.
3.   Kleinrock, Leonard.  Queueing Systems.  New York:  John Wiley and Sons,
     Inc., 1975.
4.   Viper Operational Test II Test Report.  U.S. Army Operational Test and
     Evaluation Agency and U.S. Army Infantry Board, 1981, FTR-OT-279.
5.   Young, John P., and Ackles, Andrew T., et. al., Project Pinpoint; Disclosure
     of Antitank Weapons to Overwatching Tanks.  Chevy Chase:  John Hopkins
     University, 1958.



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