15.1 OBJECTIVES AND INTRODUCTION
1. Be acquainted with fuze classification.
2. Know the basic functions of a fuze system.
3. Know the types of target detection and recognition devices.
4. Understand the principles of operations and design of proximity fuzes.
5. Understand the basic function of an S&A device.
6. Understand the concepts of reliability and redundancy as they apply to safety and arming.
7. Be able to determine the functional reliability of a fuze system.
A fuze is a weapon subsystem that activates the warhead mechanism in the vicinity of the target and also maintains the warhead in a safe condition during all prior phases of the logistic and operational chain.
The fuze is essentially a binary state mechanism. In the context of weapon system hardware, a fuze and warhead are unique in that they are expected to remain functionally quiescent until a bona fide target is encountered, and then to function as intended in a fraction of a millisecond. Guidance systems may recover from transient malfunctions; target-tracking radars may experience numerous false alarms without significantly compromising their utility; and missile airframes may flex and recover, but the fuze-warhead process is singular and irreversible. The quality required of fuze designs is usually specified by two values: functional re-liability, which ranges typically from 0.95 to 0.99 for complex missile fuzes, and to 0.999 for projectile and bomb contact fuzes; and safety reliability, for which a failure rate not greater than 1 in 106 must be proved prior to release of items for service usage.
15.2 FUNCTION OF THE FUZE SYSTEM
The weapon fuze system has five basic functions that it can perform:
(1) Keep the weapon safe
(2) Arm the weapon
(3) Recognize or detect the target
(4) Initiate the detonation of the warhead
(5) Determine the direction of detonation (special fuzes only)
A typical fuze system that incorporates these five basic functions is depicted in figure 15-1. These functions will be described in greater detail in the following sections.
15.2.1 Safing and Arming
When prehistoric man first dropped his club on his toe, he realized that his own weapon could be dangerous to himself as well as to his enemies. With today's highly destructive weapons, there must be a high degree of assurance that the weapon will not detonate until it has reached the target that it is intended to destroy. This assur-ance is provided by the safing and arming device (S&A).
The S&A device is a fuze component that isolates the detonator from the warhead booster charge during all phases of the weapon logistic and operational chain until the weapon has been launched in the intended mode and has achieved a safe displacement from the launch vehicle. Then, at that point in the trajectory, the S&A device removes a barrier from the explosive train, allowing the detonator thereafter to initiate the warhead.
Some S&A devices function by measuring elapsed time from launch, others ascertain distance traveled from the launch point by sensing and doubly integrating the acceleration experienced by the weapon. Some devices sense and integrate air speed or projectile rotation (centrifugal force), while still others may sense several stimuli characteristic of the weapon trajectory, such as rocket motor gas pressure and acceleration. To maximize the safety reli-ability of a fuze, the S&A device must ensure that the forces it senses will be unique to the weapon when deployed, and cannot be intentionally or accidentally duplicated during ground handling or prelaunch operations.
Most missiles incorporate an S&A device that utilizes acceleration-sensing. This device senses the acceleration from the rocket motor. The rocket motor boost may only induce a 10-g force, while the weapon dropped from a sling may easily experience 500-g shock forces. Therefore, another feature must be used to prevent arming should the weapon be dropped. This salient feature is that acceleration-sensing systems must experience acceleration for a protracted period of time, such as for at least one second or at least 10 seconds. Such a system is illustrated in figure 15-2.
In this device a g-weight within the S&A drives the "out-of-line" explosive lead into alignment at a rate controlled (typical-ly) by a Geneva escapement, the rate of which is not very sensitive
to the acceleration magnitude. The "intent to launch" signal, by operating on the armature of a solenoid, retracts the launch latch as the weapon experiences forward acceleration. The g-weight tends to move aft against the spring, but its rate of movement is retard-ed by the Geneva escapement, which functions like the escapement of an alarm clock. After a period of time the detonator, the "out-of-line" explosive lead, and the output explosive lead align and form a continuous explosive chain from the detonator to the warhead boo-ster charge. When the g-weight reaches that position, a second pin is pushed by a spring into a detent in the g-weight and locks it in the armed position.
If the rocket motor is faulty or such that sufficient ac-celeration is not sustained for the expected time, then the aft spring will return the g-weight rapidly to its original position (the Geneva escapement has, in effect, a ratchet that permits rapid
reverse movement), and the launch latch will be inserted into the g-weight again, locking it into the safe position. This ensures that the warhead will not detonate should it unexpectedly fall short, due to motor failure.
The linear-motion g-weight acceleration integrator, while very rugged, has the functional disadvantage that during lateral acceleration of the missile, which may exceed 30-g in magnitude, the frictional force between the g-weight and the tube is high. This retards the axial motion of the g-weight and extends the arming distance. In a more efficient design, linear motion is con-verted into rotary motion of the g-weight. A metal disk mounted eccentrically on a transverse shaft rotates as the missile accel-erates, aligning the explosive train.
To obtain the desired safety reliability in this example, there are several redundant components: the launch latch, the Geneva escapement, and the G-weight with its spring. If any one should fail (e.g., should the launch latch shear if the weapon were dropped), another would still prevent inadvertent arming (the Geneva escapement would prevent the g-weight from moving aft). This is the type of redundancy that is found in all S&A devices.
S&A devices are made of extremely high quality components and are designed to have a probability of safety failure of not greater than 1 in 106. That is the usual safety level required of Navy missile S&As. More than 350,000 have been fielded for fleet use without a single safety failure.
The discussion so far has emphasized keeping the weapon safe before it reaches the target. It may be necessary to include an additional S&A device in the firing path to safe the weapon if the intended target is missed. An example would be an antiaircraft projectile or SAM that could fall on friendly territory if an air-borne target were missed. To preclude this possibility, a surface-to-air missile could have an additional timer S&A device that would normally arm. This would allow firing path continuity until the expected elapsed time from launch to target intercept is exceeded, at which time the device will safe the missile.
An alternative to using a timer S&A device would be to place an additional timer firing device in the fuze system in addition to the normal target-sensing device. If the target is missed, then the alternate timer device would send the fire signal for detona-tion. The timer setting would be based on a time greater than nor-mal intercept, but would detonate while the weapon was still safely airborne. This alternative design method of increasing the safety reliability is found in most antiaircraft projectiles.
Although the fuze with its S&A device is the primary safety component of the weapon, it must be realized that the warhead is not insensitive to influences other than fuze initiation. The chemical high explosives used in both conventional and nuclear war-heads can be detonated if subjected to enough heat and energy from external sources. Combat or accidental detonations or fire can provide this required energy.
15.2.2 Target Detection and Recognition
Target detection and recognition must occur either when the target is close enough to be contained within the damage volume of the warhead, or such that the proximity fuze can predict when this con-dition will occur. This function can be accomplished by several types of mechanical or electrical sensor devices. The specific de-vice used classifies the type of fuzing system. Once the target has been detected or "sensed," the detection or recognition device either sends, or predicts when to send, a fire signal to the det-onator. There are four basic categories of these devices:
220.127.116.11 Impact or Contact--This sensing device detects the first impact of the weapon with an object. Its output initiates the detonator. Typical sensor mechanisms include displacement of an inertial mass, stressing of a piezoelectric crystal, short-circuit-ing of a coaxial transmission line, and interruption of an elec-trical circuit. Point detonating fuzes are of this type. A delay mechanism can also be incorporated that provides a short detonation delay (in microseconds) after weapon contact and allows for weapon penetration of the target to maximize damage effect.
18.104.22.168 Ambient--Although not able to detect the physical pres-ence of the target, it can sense the unique environment in which the target can be found, such as water depth. This type of sensing services would normally be found on depth-bomb and depth-charge weapons.
22.214.171.124 Timer--After a predetermined elapsed time, a timing de-vice will send a fire signal to the detonator. The "sensing" or "detecting" of the target is predetermined by the user in that a preset elapsed time is based on calculations of when the target is expected to be within the damage volume. Gun projectiles use this type of fuzing. Bombs can have variable time fuzes that can be set to go off from minutes to hours after striking the ground. See figure 15-2.
126.96.36.199 Proximity--This device does not require target contact, but will sense the physical presence of the target at some dis-tance. It sends a fire signal to the detonator when the target is predicted to be within the damage volume of the warhead. Proximity fuzes are called target-detecting devices or TDDs.
15.2.3 Warhead Initiation
A warhead usually contains a powerful but relatively insensitive high explosive that can only be initiated by the heat and energy from a primary explosive. The primary explosive is a component of the fuze subsystem and is normally loaded in the detonator. If the detonator is designed properly, it can only be activated by a unique fire signal received from the target-sensing device. A det-onator can be designed to activate when it receives either elec-trical energy (high voltage) or mechanical energy (shock or stab) from the target sensor.
15.3 FUZE SYSTEM CLASSIFICATION
Several fuze system classification conventions are employed in present Navy practice. Since fuze designs vary widely according to weapon characteristics and mission, one classification convention groups them by weapon application:
(1) Gun projectile fuzes
(a) For rotating ammunition
(b) For nonrotating ammunition
(2) Rocket fuzes
(3) Bomb fuzes
(4) Mine fuzes (called "exploders")
(5) Missile fuzes
(d) Surface-to-surface (subsurface to surface)
(6) Torpedo fuzes (called "exploders")
A second classification system is used that reflects the manner of fuze operation:
(1) Proximity fuzes (VT fuzes)
(2) Time fuzes
(3) Point detonating fuzes (impact)
(4) Delay fuzes
(5) Command detonate fuzes
15.4 PROXIMITY FUZES
By far the most complex class is proximity fuzes. Proximity fuzing had its origins in England early in WWII. Operations research an-alysts, pondering how to increase the effectiveness of their anti-aircraft artillery, calculated that a proximity-sensing fuze car-ried on the projectile could make the German bomber effectively 10 times as large as its physical size by detonating the projectile in the vicinity of the target rather than at a fixed flight time of the projectile. Thus, of those projectiles that would intercept the target at a range where damage could be inflicted, ten times as many would be effective in damaging or destroying the target in comparison variable-time, or VT, fuzed projectiles. Today, the incidence of direct hits by guided missiles is higher than for unguided projectiles, but the original principles still hold true.
Proximity fuzes accomplish their purpose through "influence sensing," with no contact between the warhead and target. These fuzes are actuated by some characteristic feature of the target rather than physical contact with it. Initiation can be caused by a reflected radio signal, an induced magnetic field, a pressure measurement, an acoustical impulse, or an infrared signal. A prox- imity fuze is classified by its mode of operation, of which there are three: active, semi-active, and passive. These three modes are illustrated in figure 15-6.
15.4.1 Electromagnetic Proximity Fuzing.
Conceivably, all portions of the electromagnetic spectrum could be used for target detection. Practically, however, considerations of propagation, attenuation, and other parameters affected by the rad-iation determine the applicability. The portions of the spectrum having the greatest utility are radio, radar (microwaves), and in-frared. An electromagnetic fuze, operating particularly in the radio and radar region, may be constructed to operate much like a miniature radar set. It must transmit, receive, and identify electromagnetic pulses. The proper received signal initiates the detonator. The basic active electromagnetic proximity TDD has the following components:
(1) A transceiver composed of solid-state electronics as-semblies, which is capable of delivering the required power for transmission and sensitive enough to sense the weak signal return.
(2) Amplifying circuity to magnify the return signal, so that it will activate the firing circuit and initiate the detonator. The receiver and amplifier circuits are designed to select the correct signal.
(3) A power supply to generate and provide electrical power for the fuze.
188.8.131.52 Surface Weapon Application. Some weapons used against surface targets, such as bomblets delivered to the target area in canisters called cluster bomb units (CBU) and fuel-air-explosive (FAE) weapons, employ proximity fuzes to deploy and disperse the payload at a predetermined height. Anti-personnel weapons having unitary warheads are more effective when detonated above the target area than on contact. Proximity fuzes for these applications may function as radio or electro-optical altimeters or as slant-range-sensing devices that measure range to the surface at the projected point of weapon impact.
One means of signal selection makes use of the radar principle, in which the elapsed time between a transmitted and received pulse is a function of range between target and weapon. A range-gate circuit set for a given distance will pass the signal to initiate the warhead when the elapsed time reduces to a predetermined value. The maximum range gate, which renders the fuze insensitive to effects that are farther away in range, is called the range cut off (RCO) of the TDD sensor. For example, with respect to backscatter from precipitation, the magnitude of fuze response is proportional to the volume of rainfall interrog-ated within an "in integration period." When this volume is re-stricted by the range cutoff, fuze response to rain return is re-duced by an amount proportional to the reduction in volume of rain interrogated. This mechanism is especially important in the en-gagement of a low-altitude target, where the sea surface is a highly efficient reflector of radar waves.
Another means makes use of the doppler principle, in which
the frequency of the received signal varies as a function of the relative velocity between the weapon and target. This permits the classification of targets according to their radical velocities, which is useful in the selection of a primary target within a group of signals from a variety of sources. The doppler frequency can also be used to determine when to detonate the warhead. If the encounter is head-on, the doppler would be a relatively high up-shift, in comparison to predetermined levels set within the fuze circuitry, and detonation of the warhead would need to be immediate to ensure hitting the target and not going behind it. If the en-counter is from the rear, as in a chasing situation, the doppler shift would be relatively low, and therefore a delay in detonation might be desired to ensure a hit. The point of detonation could occur when the doppler shifts from an up to a down doppler or at the point of closest approach.
184.108.40.206 Missile Fuze Applications. In air-target weapon applic-ations, the main function of the proximity fuze is to compensate for terminal errors in weapon trajectory by detonating the warhead at a point calculated to inflict a maximum level of damage on the target. Because of the kinematic relationships of the weapon, the target, and the warhead kill mechanism following detonation, the preferred point of detonation is not, in general, the point of clo-sest approach of the weapon to the target. Instead, the system engineer strives for a fuze design that will adaptively initiate the warhead within the so-called "lethal burst interval" for each trajectory that his weapon is likely to experience in future oper-ational usage. The lethal burst interval is defined as that inter-val along the trajectory in which the warhead can be denoted so as to hit the target in the vulnerable area. That ideal state is of course never realized in practice, where idealism must be tempered by practicality. As a compromise, the engineer derives a design that is practical, affordable, and that will maximize the number of lethal detonations in a representative sample of all postulated encounters. The actual point of detonation realized in a given encounter is the result of fuze design parameters, weapon vector velocity, location of the encounter in the weapon performance en-velope, burst control logic, and a wide variety of other contrib-uting factors such as active or passive countermeasures and envir-onmental effects.
As an example of this, realize that tactical missile warheads are not so powerful that they will devastate the target if detonat-ed anywhere in its vicinity. Also, warheads cannot be made larger and heavier without seriously compromising missile speed, altitude, range, and maneuverability. Therefore, the fragments ejected by the warhead must be delivered onto those areas of the target that are most vulnerable to damage: the cockpit, the engine compressor stages, and the flight control system. This requires sophisticated fuzing, with precise burst control.
Furthermore, to maximize its lethal range, the warhead is designed such that ejecta are confined to a narrow zone in the missile pitch plane. Thus, a lethal density of fragments is main-tained to ranges much greater than if the fragments were dispersed isotropically. The proximity fuze is called upon to solve this convergence problem--i.e., converging the narrow fragment pattern and the limited vulnerable regions of the target. Figure 15-7 illustrates how this is accomplished. The figure represents a missile approaching the target from the rear and passing either above or below the target (i.e., not a direct hit). Target vulnerable areas or regions that must be hit to ensure a kill are also depicted.
At Point A the proximity fuze detects the first extremity of the target that penetrates its sensory pattern. This initiates a series of events that will result in warhead detonation at Point B. The time delay that permits the missile to traverse from Point A to Point B is varied as a function of closing velocity in accordance with the equation
T = M - N
where Vc is the closing velocity in meters per second, T is in mil-liseconds, and M and N are either constants or variables, depending on the complexity of the fuze, with their units chosen accordingly. When the warhead is detonated at Point B, the vector sum of missile velocity, warhead expansion velocity, and target velocity will cause the warhead ejecta to impact the target in Region C. This illustrates a successful warhead detonation, as the fragments im- pact some of the vulnerable regions of the target.
It should be evident immediately that the terminal encounter situation involves the interplay of many parameters that are depen-dent upon target characteristics, missile characteristics, and pos-itional relationships at the time of missile launch. The degree of variability and uncertainty in these parameters is increased by the maneuverability and countermeasures capability of the target. Since most missiles are capable of all-aspect attack, and the tar-get's velocity can vary over a wide range of values, the closing velocity used in the time delay equation may range from 180 to 1,800 meters per second, or more. The spectrum of targets intended for the missile will encompass targets that may be small, medium, or large in physical size, but their velocity capabilities overlap to such an extent that a time delay selected for a given Vc might be successful for one target and a failure for another. Further-more, it is possible for very long targets in high-crossing-angle encounters to present only a square meter or less of vulnerable area to the warhead. Thus, gross target dimensions are not very useful as measures of where the warhead should best be detonated.
Being sensor devices by nature, fuzes are subject to a wide spectrum of disturbing influences in the real-world tactical en-vironment. One of the foremost prerequisites of good fuze design, therefore, is to devise a sensor system that discriminates bona fide target return from all distracting influences, whether they take the form of electronic or optical countermeasures, intense electromagnetic radiation levels characteristic of fleet environ-ments, chaff, precipitation, out-of-range targets, or radar clutter such as occurs in missile flight at low altitude.
15.4.2 Magnetostatic Fuze Applications.
Magnetic sensors, such as magnetic anomaly detection (MAD), measure changes in the earth's magnetic field or the presence of a source of magnetic flux. In the case of fuze systems,a magnetic sensor is designed to recognize an anomaly and ultimately cause the fuze and safety and arming (S&A) device to function. Such a target detec-tion device may be designed that will close a firing circuit upon a disturbance of the earth's magnetic field by one of the magnetic components of a ship, as described in Chapter 9. The target does not necessarily have to be moving, although an S&A device may be employed that requires a certain rate of target movement. Mines that employ this principle of fuzing are commonly used. They are known as dip-needle, influence mines.
Another type of TDD employed with mines is an inductor mechan-ism, frequently called a search cell. This device employs the principle that a magnetic field induces current flow in a conductor as the field changes relative to the conductor. The small voltage induced in the search cell is amplified and then caused to energize the firing circuit, which in turn initiates the detonator. The ex-treme simplicity of this device makes it highly reliable and diffi-cult to counter.
Magnetostatic fuzing is also used for subsurface targets.
The magnetic field disturbance fuze for subsurface targets is also actuated by a change in the surrounding magnetic field. Any change in the magnitude of the magnetic field activates the fuze. A mag- netic-type fuze provides the possibility of damaging a target with-out a direct hit. This is important, as the damage potential is greater when the explosion of the warhead takes place several feet below the hull, rather than at the side or near the surface of the water. The most advanced methods of fuze initiation operated by a ship's magnetic field employ an electromagnetic detecting system. Such a system operates on what can be called the "generator prin-ciple." Essentially an electric generator consists of a coil of wire rotated in a magnetic field to produce a voltage. Similarly a small voltage is developed across a coil of wire (the search coil) when it comes in contact with a moving or changing magnetic field. However, a complex problem can occur, due to the fact that the movement of the interceptor itself (torpedo) through the water creates its own change in the field gradient and initiates the fuze at an earlier time than intended. This has led to the development of the gradiometer, a device attached to the torpedo, which has two search coils approximately one foot apart and connected in opposing series. As the now magnetically balanced torpedo moves in earth's magnetic field, equal and opposite voltages are induced in the coils, and no net voltage results. In the vicinity of a steel ves-sel, the situation is different. One of the two coils is slightly closer to the vessel than the other, and a slightly different volt-age will therefore be induced in it. This difference is small, but when properly amplified, it causes the detonator to explode the warhead.
15.4.3 Acoustic Fuze Applications.
Acoustic disturbances, such as propeller and machinery noises or hull vibrations, invariably accompany the passage of a ship through the water. The intensity or strength of the sound wave generated depends upon several factors, such as ship size, shape, and type; number of propellers; type of machinery, etc. Therefore, a ship's acoustic signal is variable, and acoustic fuzes must be designed to prevent an intense signal from actuating the fuze at distances well beyond the effective explosive radius of the payload. Figure 15-8 illustrates a basic acoustic mine mechanism.
This system employs a hydrophone as a detector to sense the presence of a target. A typical hydrophone functions much the same as the human ear. A diaphragm (corresponding to an eardrum) vi-brates from the impact of underwater sound waves. These vibrations are transmitted through an oil medium to a crystal, which converts the mechanical energy to the electrical energy required to initiate the firing mechanism. The selectivity of the firing mechanism is so critical that only the pulses of the required characteristics are sent to the detonator. Selectivity is necessary because of the varied sounds that are received by the mine. To distinguish among these many sounds, acoustic firing mechanisms must possess a very selective type of hearing. For example, a 2,000-ton tramp steamer may have one large propeller turning over rather slowly, and a 2,000-ton destroyer may have two propellers turning over much fast-er. An acoustic firing mechanism can distinguish between the steamer and the destroyer, and fire on the selected target. When the firing mechanism detects a sound that has the required charac-teristics (including intensity and rate of change of intensity), the mechanism initiates the firing circuitry and fires the detonator.
Acoustic fuze mechanisms are used in torpedoes as well as mines. There are two operating modes of acoustic torpedoes, the active and passive types. The passive type has a homing device that guides the torpedo in the direction of the strongest target noise. The active type employs a sonar set that emits a series of sonic pings that are reflected back to a receiver in the torpedo. The principle is similar to that of a radar set. As the torpedo approaches the target, less time is required for a signal to travel to the target and return. At a predetermined critical distance, initiation of the firing circuit begins.
15.4.4 Seismic Fuzing
A similar type of acoustic influence sensor used in some types of mines is the "seismic" firing mechanism. This sensor is essenti-ally an acoustic fuze, but receives its threshold signal in a lower bandwidth through weapon-case vibration. These sensors can be made extremely sensitive and may provide for both land-based or in-water application. They offer advantages over the pure acoustic mine fuze in that they may be set over a wider range of selectivity and may incorporate some countermeasure features. Most new mines will use a seismic fuze with other influence fuzes as a means of ensur-ing weapon activation on a valid target and to reduce the effec-tiveness of mine sweeping efforts.
15.4.5 Hydrostatic (pressure) Fuzing.
Oceans swells and surface waves produce pressure variations of considerable magnitude. Moving ships displace water at a finite rate. This continuous water flow is measurable at considerable distances from the ship as pressure variations that normally exist in the water. Various pressure-measuring mechanisms can be used in fuzes to detect such variations. The pressure differential becomes more pronounced when the ship is moving through confined waters, but is still appreciable in the open sea, even at a considerable depth. This pressure variation, called the "pressure signature" of a ship, is a function of ship speed and displacement and the water depth. Therefore, to avoid premature firing because of wave ac- tion, pressure-firing mechanisms are designed so as to be unaffec-fected by rapid pressure fluctuations. Pressure sensors are com-monly associated with bottom mines and are extremely difficult to counter through normal influence-mine countermeasure techniques. Pressure-firing mechanisms are seldom used alone, but are generally combined with other influence firing devices.
15.4.6 Combination Fuzing.
Systems involving a combination of influences are available in most mine firing devices. The combinations of magnetic, pressure, and acoustic/seismic systems are used to compensate for the disadvant-ages of one system with the advantages of another. Mine counter-measure effectiveness can be greatly reduced through use of combin-ation fuzing. Minefield theory involves detailed and complex anal-ysis, which is beyond the scope of this text. The entire minefield must be considered as a weapon in a mining scenario, and multiple targets are programmed against it to determine the overall effec-tiveness. For the sake of simplicity, our discussion will be re-stricted to a single mine against a single target. The influence sensors described earlier may be considered individually or as a combination. Regardless of the particular influence, there is a threshold level that will activate the mine based on the sensitiv-ity setting for the weapon. This will obviously occur at some distance from the target--the distance being greater the more sensitive the mine setting. This distance is referred to as actuation distance and is depicted in figure 15-9.
It should be obvious that a mine could be so sensitively set that is could be made to detonate on a target influence such that the explosion would be outside of the range at which the mine could do damage to the target. The range at which a mine will damage a target is referred to as the "damage distance." This would also be described as similar to the circular pattern of figure 15-9. From a minefield planning standpoint, it is most important to optimize the mine setting such that the weapon does not actuate until the target is within damage range. Obviously, the actuation distance sound be less than or equal to the mine damage distance. The prob-lem becomes much more complex in actual planning. Each target class has its own associated signature as well as relative tough-ness against damage, and the ship-mine encounter is greatly influ-enced by such factors as ship heading and speed, environmental state, and orientation of mine and ship. It is impossible to de-termine all of these factors precisely; therefore, approximations are made at varying levels of accuracy. Mine actuation probabil-ities and damage probabilities have been computed based on various target and mine types, water depths, ship speeds, mine sensitiv-ities, etc., and are published as classified information for use in minefield planning methodology.
The reliability of the basic functions of target sensing, arming, and payload initiation is obviously contrary to the weapon safety function of a fuze. A fuze detonator that will reliably detonate the payload at target impact presents a safety reliability problem if it also detonates when dropped during handling.
To design a fuze to be reliably safe, a designer may compromise arming and firing reliability. A fuze detonator designed not to detonate from rough handling may also be so insensitive that the contact fuze would dud at target impact. An S&A pressure device that is designed to sense too high an airspeed may not arm in time when deployed against short-range targets. There are several methods available to the designer to increase arming and initiation reliability and also increase safety reliability without compromising the reliability of each of these paradoxical functions.
15.5.1 Functional Reliability.
Although fuze design must emphasize safety, the primary objective of the warhead is to detonate at the proper time. Therefore, the sequence of S&A and target-sensing devices must have a high proba-bility of functioning correctly when they receive their unique arming signal. Functional failure of any one of the devices in figure 15-1 would result in a dud warhead. As with any man-made device, the fuze components must be based on a sound design, a-voiding an overly complex function requirement. Before the reli-ability criteria can be assured, every new S&A device must be extensively tested. Sophisticated weapons will have S&A devices that sense and arm with such a high reliability that less than one in a thousand is expected to fail functionally. Note that a func-tional failure is not the same as a safety failure, but occurs when the component fails to operate as designed when proper environ-mental conditions exist.
Functional reliability of the entire fuze system can be in-creased by having more than one type of target sensor placed in parallel and more than one detonator in the S&A device, as shown in figure 15-10. Most missile fuze systems have one or more backup contact sensors in addition to their proximity sensor. Thus, the probability of warhead functioning is increased. This leads to another basic principle in fuze design, which can be stated as:
A redundant increase of the number of similar components placed in parallel in the firing path will increase the arming and firing reliability.
15.5.2 Safety Reliability
As pointed out earlier in the safety and arming discussion, safety reliability depends on the successful sequential operation of re-dundant components. Failure of any component in the series results in overall failure to reach an "armed" status.
Thus, a similar fundamental principle in fuze design can be stated as:
A redundant increase in the number and types of devices
placed in series in the firing path increases the safety
reliability of a fuze.
15.6 PROBABILITY THEORY
The performance of complex systems such as weapon fuzes can be de-termined through application of probability theory. The principles of parallel operation as stated above, as well as those of series systems, lead to a method of determination of total system relia-bility regardless of the number or arrangement of components. Two fundamental principles of probability theory are used in determin-ing fuze reliability: statistically independent events and mutu-ally exclusive events.
15.6.1 Statistically Independent Events
Two events, A and B, are independent if the probability that A oc-curs is unaffected by the occurrence or nonoccurrence of B, and vice versa. The probability of several statistically independent events occurring simultaneously is the product of the probabilities that the individual events occur. Thus, the probability that e-vents A and B both occur, given that their probabilities of occur-rence are P(A) and P(B) is
P(A and B) = P(A) X P(B)
15.6.2 Mutually Exclusive Events.
The probability of several mutually exclusive events occurring is the sum of the probabilities of each event. Two events are said to be mutually exclusive if the occurrence of one event prevents the occurrence of the other. If events A and B are mutually exclusive and if their probabilities of occurrence are P(A) and P(B), then the probability that either A or B will occur is
P(A or B) = P(A) + P(B)
Mutually exclusive events are not independent since, by definition, if one occurs, the other cannot, or P(A and B) = 0.
15.6.3 Series Systems.
Suppose that a system consists of two independent components ar-ranged in series. That is, for the system to operate properly or be successful, each of these independent components must operate properly and in sequence. Schematically this system can be de-picted as follows:
---- 1 ---- 2 ----
The effect of each component's success or failure on total system performance can be tabulated as follows:
Component 1 S S F F
Component 2 S F S F
System S F F F
Notice that the system is successful only if both of the components are successful. All other possible situations lead to system fail-ure. In order to calculate the probability of this system's suc-cess, it is only necessary to calculate the probability that both components are successful. Letting S1 and S2 stand for the prob-ability that component 1 and component 2 are successful respec-tively and noting that these components are independent, a simple expression for the probability of system success results:
P(S) = S1 X S2
Also, since the qualities of success and failure are mutually ex-clusive and cover all possible system outcomes.
P(S) + P(F) = 1
P(F) = 1 - P(S) = 1 - (S1 X S2)
If a system has more than two components in series, its probability of success is again simply the product of the individual component success probabilities:
P(S) = S1 X S2 X S3 X . . .
P(F) = 1 - P(S) = 1 - (S1 X S2 X S3 X . . .).
As an example, the S&A device of figure 15-2 has three independent components that must operate in series for arming to occur. The system can be modeled as follows:
The probability of successful arming for this device can be cal-culated as
P(S) = S1 X S2 X S3 = .98 X .97 X .99 = .9411
Also, the probability of failure is
P(F) = 1 - P(S) = 1 - .9411 = .0589.
Note, calculations are usually carried out to 4 significant places and the resulting probability (in series systems) is less than any individual original probability.
15.6.4 Parallel Systems.
Suppose that a system consists of two independent components ar-ranged in parallel. This means that for the system to be success-ful, only one of the components must be successful. Schematically, this system can be depicted as follows:
The effect of each component's success or failure is illustrated in the following table:
Component 1 S S F F
Component 2 S F S F
System S S S F
Notice that for a parallel system, the only way that the system can fail is if all the individual components fail simultaneously. Cal-culating the probability of system success is rather complicated since it is the probability that component 1 and component 2 are successful or component 1 is successful and component 2 fails or component 1 fails and component 2 succeeds. It is much easier to calculate the probability that the system fails, which is:
P(F) = F1 X F2
Then, since system success and failure are mutually exclusive,
P(S) = 1 - P(F) = 1 - (F1 X F2)
For example, consider a system consisting of two detonators placed in parallel, each with a success probability of .95.
The probability of success for this system is given by
P(S) = 1 - (F1 X F2)
Now, since the qualities of success or failure for each individual component are mutually exclusive
S + F = 1
F = 1 - S
P(S) = 1 - (F1 X F2) = 1 - [(1 - S1) X (1 - S2)]
= 1 - [(1 - .95) X (1 - .95)]
= 1 - (.05 X .05)
= 1 - .0025
15.6.5 (Fuze System Reliability: An Example)
A particular type of ammunition used for shore bombardment against troops in the open is designated as VT-NSD (variable time-not-self-destruct). The fuze system for this type of projectile has a prox-imity sensor designed to detonate 100 feet from the ground and an impact sensor as a backup, should the proximity sensor fail. The following diagram is a schematic representation of the entire fuze system, and each component's probability of operating successfully is given.
S1 = .94
Detonator S&A Device
S3 = .99 S4 = .95
S2 = .98
To calculate the fuze system reliability (probability of success), it should first be noted that this is a combination of parallel and series elements. If the probability of the TDD func-tion success is first calculated, then this system is reduced to three functional elements in series. Calculating the probability of the TDD function success,
PTDD(S) = 1-PTDD(F) = 1 - (F1 X F2) = 1 - [(1 - S1) X (1 - S2)]
Now, calculating the overall success probility of three functional elements in series,
P(S) = PTDD(S) X S3 X S4 = (.9988)(.99)(.95)
Thus, this fuze system will successfully detonate the warhead 94% of the time.
As previously discussed, a safety failure is different from a func-tional failure. A safety failure occurs when the components, for some reason, fail to keep the fuze in a safe condition when so de-sired, and premature arming occurs. Thus, a safety failure is said to have occurred if the weapon becomes armed other than through its normal firing sequence. From this definition, it can be seen that a safety failure to occur, the series components of a safety and arming device must simultaneously malfunction in such a manner that the weapon is armed. Since the probability of a component of an S&A device having a safety failure is normally very small, the probability of three or four components having a safety failure simultaneously is minute. Thus, again, series redundancy leads to safety reliability.
The fuze is that functional subsystem of the ordnance system that actuates the warhead in the vicinity of the target and maintains the weapon in a safe condition during all prior phases of handling and launching. All fuzing systems perform four basic functions: safing, arming, recognition or sensing of the target, and initia-tion of the warhead. All fuzes contain some type of target-sensing device, with all missiles having an electromagnetic proximity sen-sing device called a TDD. TDDs are classified according to their mode of operation: active, semi-active, or passive. All fuzes contain S&A devices that keep the weapon safe through a series of redundant components until the weapon has sufficient separation from the launch point. At that point the S&A device removes a barrier from the explosive train, arming the weapon. The redundant components provide an improved safety and functional reliability for the weapon.
Bulgerin, H. A. "Comments of Fuze Technology." Unpublished notes.
Burns, R. L., Cdr., USN. "Notes of Mine Warfare." COMMINWARCOM, Charleston, S.C., 1983.
Commander, Naval Ordnance Systems Command. Weapons Systems Fundamentals. NAVORD OP 3000, vol. 2, 1st Rev. Washington, D.C.: GPO, 1971.
Weapons and Systems Engineering Department. Weapons System Engineering. 6th ed. Annapolis, Md.: U.S. Naval Academy, 1984.