Overview Ballistic Missile Defense
Air and missile defense weapon system designs are typically
based on an architecture that integrates an acquisition and tracking sensor
used for fire control, a battle management command and control system, and
guided missiles. Figure 1 illustrates the major engagement components and
events that may comprise a Ballistic Missile Defense (BMD) engagement detection
and tracking of a threat missile may involve several sensors, which could be
space, land, and/or sea based. Remote sensor data may be received, processed,
and transmitted to a launch platform via a battle management, command, control,
and communications (BMC3) node.
Upon determination of an engagement solution,
the defending missile is launched and guided on an intercept path until a kill
vehicle (KV) is released for the final phase of the mission. The seeker on the
KV acquires the threat lethal object and establishes a track for guidance. The
KV’s divert system removes the trajectory errors that remain after the earlier
portions of flight and responds to guidance commands derived from seeker
measurements. For exoatmospheric intercepts, the onboard sensor is typically an
IR seeker, whereas a RF seeker is often used for endoatmospheric intercepts.
The development of a new weapon system concept typically involves a series of
trades that derive fire control sensor, BMC3, and missile key performance
parameters.
These performance parameters characterize, for example, the
detection range and track accuracy of the fire control sensor, communications
time delay, the time of flight of the missile, and the ability of the missile
terminal guidance to remove system errors. Depending on the particular weapon
system needs, the tradable parameters may include all aspects of the fire
control sensor, BMC3, and missile. In some cases, only missile parameters may
be tradable as constrained by an existing launch system. In all cases, the
starting point is the definition of a mission, the threat characteristics, operating
constraints such as potential missile launch locations, and the portions of the
system that must remain unchanged because of programmatic decisions.
MISSILE CONCEPT OPTIMIZATION
Paralleling the performance attributes in Fig. 2,
optimization of the missile concept can be separated into three loosely coupled
subproblems as shown in Fig. 3: (i) kinematic reach, (ii) error containment,
and (iii) lethality. Decoupling is possible because optimization of the booster
configuration to minimize flight time depends on KV mass but not the specific
KV configuration. Kinematic reach is the most fundamental performance criterion
because the threat trajectory must be within both the missile range and speed
capabilities for the intercept to be possible. For specified missile launcher
and system timeline constraints, the booster can be optimized to maximize the
reach to threat trajectories for a KV mass limit.
Optimization of the booster
configuration for a given KV mass is discussed in the next section. Given
kinematic reach, the system errors must be removed to intercept the threat. A
larger KV mass degrades missile kinematic reach but allows more capable seeker
and divert and attitude control system (DACS) capabilities to remove handover
error. Thus, the second optimization is to minimize KV mass while still
achieving error containment. This optimization mostly becomes a trade between
the DACS mass and the seeker mass. DACS mass translates to KV divert maneuver
performance (i.e., acceleration or velocity change, whereas seeker mass
translates to seeker acquisition range. As seeker acquisition range is
increased, less divert performance is needed because more time is available to
remove error. There is some coupling between the booster and KV optimization
problems. The booster and KV capabilities are both optimized when the kinematic
reach and error containment are brought into balance. If error containment
cannot be achieved for certain trajectories given the KV mass limit, then some
kinematic reach may need to be sacrificed to bring the concept into balance.
The goal is to ensure that errors are contained for all potential intercept
points. Conversely, if all of the mission threat trajectories are reached with
excessive containment margin, then other portions of the system design such as
engagement support quality or KV mass and missile size might be relaxed. Once a
basic KV configuration is determined, endgame lethality depends on the ability
to determine and steer out remaining guidance errors. This is mostly a trade
between seeker resolution and acceleration capability of the KV. The result of
this trade can affect the KV optimization because both the seeker resolution
and KV acceleration parameter selections might influence KV mass, which may
require a rebalance of the KV DACS and seeker capabilities.
KINEMATIC REACH
To establish missile kinematic performance requirements for
a given mission, the first step is to develop several optimized booster
concepts that span the allow able missile size and mass trade space given
launcher constraints. For each of these booster concepts, the mass and volume
of the KV is allowed to vary parametrically. Once the configurations are
developed, a coverage analysis identifies the maximum KV mass that can be
tolerated for each concept and still meet the threat trajectory engagement
goals. This analysis will establish missile kinematic and KV mass thresholds
for each missile concept. The missile kinematic threshold can be expressed in
terms of a minimum booster burnout velocity (Vbo).
Booster Optimization
The booster concept
is developed with a multidisciplinary system-level missile design optimization
tool called ORION (Optimization of Rockets for Intercept OperatioNs), which was
written at the Johns Hopkins University Applied Physics Laboratory (APL). ORION
integrates physics-based and empirically benchmarked models of propulsion,
aerodynamics, payload packaging, and vehicle kinematics for single- or multi
objective booster optimization and relies primarily on genetic algorithms to
determine the optimal solution. Modern computational resources have now enabled
multidisciplinary, system-level analysis and design optimization.
In a
multidisciplinary design optimization approach, complex system models are
developed by integrating detailed models of various subsystems early in the
design phase. Subsystem design parameters are then varied, with their
interactions observed at the system level, leading to truly optimized system
designs. ORION, a multidisciplinary design optimization tool for missile
propulsion systems, provides the capability to comprehensively observe the
impacts of missile subsystem interactions earlier in the design evolution than
previously possible.
Propulsion Model
The propulsion system
model uses physics-based and empirically benchmarked calculations to provide
the capability for medium-fidelity stage and motor characterization. A solid
rocket motor modeling and design tool developed by APL, called ARIES (Analysis
of Rockets for Initial Exploratory Studies), is used for this purpose. The
motor/stage model accepts an input list whose components generally fall into
one of four categories: (i) propellant; (ii) nozzle assembly; (iii) case
assembly; or (iv) stage assembly. The inputs consist of propellant formulation
and ballistic properties, as well as certain dimensions, masses, and material
properties of various components. ARIES calculates motor component dimensions
and masses and, in addition, calculates motor interior ballistics, producing
time traces of chamber pressure, thrust, and expelled propellant mass. ARIES
primarily follows textbook principles for design calculations and performance
predictions. Motor performance is calculated on the basis of a lumped-parameter
ballistics code developed at APL.
Nosecone and Aerodynamics
The nosecone model in ORION allows the user to choose from
five different standard nosecone shapes: conical, tangent ogive, Kármán ogive,
LV-Haack, and power law. Nosecone length, base diameter, bluntness, thickness,
and material density are input. ORION then solves for the outer mold line,
surface area, and mass of the nosecone. Thermal analysis is performed
separately to ensure the nosecone provides adequate thermal protection of the
KV.
Boost Control
The design of the system used to maintain airframe stability
throughout flight has a significant impact on the overall missile concept.
Traditional types of control systems include aerodynamic surfaces, attitude
control systems (ACSs), thrust vector control systems, or some combination
thereof. The level of control required will determine the actuator type, size,
and mass, which in turn will impact the overall missile kinematic performance.
Thus, control system design is coupled to the booster optimization process
described above. Key events that drive the design of the control system are
stage separation, coast periods, and upper-stage maneuvers. A stage separation
occurs when a spent stage separates from the rest of the missile, which induces
destabilizing conditions in the form of tip-off angles and angular rates. The
control system must maintain airframe control during stage separation. This
function is called capture.
KV Configuration
The most commonly used KV configuration consists of a
hard-mounted seeker and a cruciform DACS. The divert system provides the
lateral motion for the KV, and the ACS provides the angular control to
stabilize seeker pointing and control divert direction. The design of the ACS
can be simplified if the center of gravity of the KV is aligned with the divert
thrusters and remains aligned throughout operation. This can generally be
achieved by positioning some of the avionics components aft of the DACS. This
is called a split KV configuration as opposed to a unitary layout. Here the
trade is between DACS and KV packaging complexity.
DACS Constraints
the traditional DACS,
the two primary propellant options are hypergolic liquids and solids. Hypergolic
propellants typically consist of a fuel and an oxidizer that spontaneously
ignite when they come into contact with each other. In addition, they are
extremely toxic and/or corrosive, making them difficult to handle. Thus, liquid
fuels have handling and safety concerns, which lead to higher infrastructure
and leakage mitigation costs. On the other hand, a liquid-propellant DACS can
be designed to ignite reliably and repeatedly, and it is a relatively mature
technology. There are four major types of solid-propellant DACSs (SDACS). The
first is an extinguishable system, which can be stopped and started as
required. Among the options, the extinguishable system is the least mature
technology (lowest technology readiness level, or TRL) and highest risk. The second
type SDACS uses multiple pulses. In this system, two or more divert pulses are
contained in a single pressure vessel. This design is a medium TRL and risk
option. The third option is a modular multiple gas generator design. The
generators can be fired in pairs for each divert event to keep the center of
gravity aligned with the divert plane as discussed in the previous section. For
example, three divert events require six gas generators. This approach has a
higher TRL and lower risk than the first two options. One of the drawbacks of
this design is the low packaging efficiency, which results in a larger DACS
space envelope compared with the other options. The fourth type, throttleable
SDACS, is similar to the extinguishable system except the thrust can only be
turned down to a lower level rather than completely turned on and off. This
type of system has the highest TRL and lowest risk, but that can depend on the
specific requirements. The final selection of a DACS configuration depends on
the required operating time, divert capability, and mass while considering risk
and cost.
Seeker Constraints
The IR seeker
detects, acquires, and tracks objects of interest and selects which object
should be intercepted. At a basic level, the IR sensor consists of optical com
Divert ponents that focus IR radiation, which is emitted or
reflected from distant threats, onto an array of IR sensor elements, or pixels,
that make up a focal plane array (FPA). There are several sensor and threat
properties, or parameters, that will affect the design of the IR sensor.
• Aperture: The physical aperture diameter is the diameter
of the IR sensor. A larger aperture will improve seeker performance for two
reasons. First, more IR radiation will be accepted into the sensor if the
aperture is larger, increasing sensitivity. Second, the ability of an optical
system to focus radiation onto a small spot will improve with larger aperture,
so seeker resolution will also improve with larger aperture. However, a larger
aperture will require a larger and more massive seeker and thereby a more
massive KV. Note the design of the optical system may cause blockage, which
reduces the effective size of the apertur.
• Waveband: The IR sensor detects radiation in the IR region
of the electromagnetic spectrum, which extends from ~2 microns to a few tens of
microns. Threats will emit IR radiation according to the blackbody radiation
equation, with the wavelength of the peak of the emission spectrum depending on
the threat temperature. Colder threats will emit radiation that peaks at longer
wavelengths. For example, room temperature threats, around 300 K, will emit a
spectrum that peaks around 8–9 microns, so threat properties must be considered
in selecting the seeker operating waveband.
• FOV: The FOV is the
angular extent observed by the seeker. A wider FOV allows the seeker to
simultaneously observe objects with increased spacing or to find an object with
increased location uncertainty. The former capability will affect the time at
which threat selection must be accomplished, whereas the latter will affect the
capability of the interceptor to contain a threat within its FOV at
acquisition.
• Instantaneous FOV (IFOV): The IFOV is the angular width
observed by a single pixel of the sensor array. A smaller IFOV is generally
better because it will allow increased resolution, which will enable the seeker
to resolve multiple threats earlier, allowing more time for endgame guidance.
• Number of pixels or FPA format: For a square array, the number
of pixels in one dimension is given by the FOV divided by the IFOV: Npixels =
FOV/ IFOV. Because it is desired to maximize FOV and minimize IFOV, a large
number of pixels is advantageous. However, very-large-format IR arrays are more
expensive to manufacture, so the maximum number
Seeker Acquisition
Range To optimize the
KV configuration, the seeker performance parameter trade space must be
characterized and related to the mass of the seeker. The relationships between
the key seeker parameters, which determine acquisition range, are shown in
nomograph form in Fig. 7. One begins at the lower left by specifying range
requirements for acquisition and discrimination and ends at the upper right
with an aperture requirement to meet the required ranges.
Seeker Field-of-Regard Containment
To acquire the threat
object, the object must be within both the seeker detection range and the
seeker FOV. The KV is commanded to point in the direction of the estimated
threat object location as provided by the fire control sensor. However,
pointing errors caused by threat tracking errors and KV navigation errors must
be contained within the seeker FOV with high probability. The KV first attempts
to acquire threats within its seeker FOV but may perform an angular search to
achieve a larger field of regard (FOR).
Analyzing the Battle Space
Before KV
optimization can be accomplished, key parameters related to the geometry
between the intercepting missile and the threat must be determined. These
parameters include: (i) handover error, expressed as initial zero effort miss;
(ii) the closing velocity, which is the relative velocity between the
intercepting missile and the threat; (iii) missile third stage burnout time;
(iv) threat burnout time; and (v) missile time of flight. To extract these key
engagement parameters, the battle space (all possible combinations of
intercept, threat launch, and threat impact points) must be analyzed using an
engagement simulation, which computes all possible intercepts where the
intercepting missile can kinematically reach the threat. The simulation also
determines the maximum possible time window during which the missile can be
launched to have a successful intercept. This window is called the launch
window.
Seeker versus DACS
With the key
parameters associated with the most stressing trajectory established, it is now
possible to balance the KV mass between the seeker and DACS. The relationships
between the divert containment parameters are illustrated by the nomogram shown
in Fig. 9. The seeker aperture size is first selected in the lower-left corner
of the nomogram. The first plot relates the seeker mass to the aperture size.
Multiple curves can be generated for different mass margin philosophies. Moving
to the lower-right plot, the seeker performance is given as a function of
aperture size. This is a roll-up of the nomogram
Physical Packaging and ACS Sizing
Now that concepts for
the major components of the KV have been developed, a physical layout of the KV
must be realized to ensure a feasible KV size. This can be done using a solid
modeling tool, such as Pro/ENGINEER or SolidWorks. In this way, the overall
package is developed and visually checked and mass properties are determined.
These mass properties are then applied in a simple six-degree-of-freedom
simulation to size the ACS. The ACS is sized to maintain stability after the KV
is ejected from the upper stage, perform the roll maneuvers before specific
divert events, maintain control during divert events, and perform the seeker
pointing functions.
LETHALITY CONSTRAINTS
The final trade area
in Fig. 3 is the seeker resolution (IFOV) versus KV acceleration needed to
ensure a hit accuracy that provides the desired level of lethality. Figure 11
shows the form of the nomograph that illustrates the trades between IFOV and KV
acceleration versus probability of hit. Given the FOV that is determined by
handover error containment analysis, the lower left plot of Fig. 11 shows the
relationship between FOV and IFOV versus FPA format. Given IFOV, the upper-left
plot of Fig. 11 defines the angular extent of the threat object as a function
of seeker aperture and the number of pixels, N, needed for recognition. The
aimpoint recognition range for an engagement is the target projected length
perpendicular to the line of sight divided by angular resolution required for
aimpoint selection. Given the closing velocity of the encounter and the
aimpoint selection range, the time-to-go at aimpoint selection is calculated
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