ABSTRACT
In this chapter, an air and missile defense (AMD) system preliminary design is evaluated against the requirements using methods described in the previous chapters and McEachron [1]� Figure 7�1 shows a graphical depiction of how the AMD battlespace unfolds from first detection to intercept assuming three interceptor variants having three different minimum ranges� Specifically, the engagement phases are as follows: range at first detection (R/detect), range at transition to a hostile track (R/firm track), range at interceptor away (R/interceptor away), range at first and subsequent nonminimum range intercepts, and minimum intercept range� This division is in fact general in that it is identical for air and ballistic targets� The timeline as presented assumes that either a subsonic or a supersonic target is being engaged at a low altitude and that the first detection occurs approximately at the horizon� At the far right, the defended area, the keep-out zone, is where the AMD system is presumed to be collocated within the indicated volume�
To complete a preliminary design level battlespace analysis, we first consider first defining battlespace depth of fire (DOF) or firepower followed by an engagement analysis� Defining the DOF requires determining for each AMD preliminary design configuration where, how many, and which interceptor variants can reach the target sets� The engagement analysis will tell us which interceptors and variants can successfully engage the targets and how many it will take to achieve the system Pk requirement� The target set is defined by speed, altitude, signature, and other environmental considerations for the battlespace evaluation� The engagement analysis requires the addition of any target defense penetration features that are uniquely intended to defeat the interceptor such as evasive maneuver [2]�
For a notional AMD system preliminary design, battlespace depth-of-fire performance is examined for three missile interceptors having three minimum intercept ranges, three radar variants, and three propagation factor environments� All battlespace depth-of-fire results are for the target para metric conditions of radially inbound speeds of Mach 1-3�5 at constant altitudes of 5, 10, and 50 m [1]� In addition, the target has a nonfluctuating, Swerling 0, radar cross section that varies parametrically from 0 to −25 dBsm [1]� All results are based on engagement timeline analysis of nonmaneuvering targets� The defensive system radar and missile interceptor launcher are colocated�
Radar parameters for the depth-of-fire results correspond to the active array architecture with the exception of pulse width, which is 5 μs, supporting a radar minimum range of 0�75 km against low-altitude targets�
This range is assumed inside the minimum intercept range for all interceptors considered� The radar detection ranges are based on single-pulse performance� It is assumed that clutter is canceled to 10 dB below thermal noise leaving the propagation factor to reduce radar sensitivity� A propagation factor of 40 dB corresponds to stressing overland engagements, while a propagation factor of 0 dB corresponds to an ideal performance reference case� Propagation factors are modeled as a constant average value at all target ranges and altitudes� Other important parameters (see McEachron [1]) used in battlespace analysis are an antenna height of 18 m, an optimum best-case combat system reaction time of 10 and 20 seconds when a kill assessment, look, is required�
The constant-altitude, inbound targets cross the radar horizon at the ranges summarized in Table 7�1� These ranges are based on a 1�62 earth model that is a good approximation for propagation conditions over a sea environment�
The radar horizon crossing ranges define the furthest range at which the target can be detected if the radar has adequate sensitivity and any clutter returns have been suppressed to levels at least 10 dB below thermal noise� Beyond these ranges, the targets are obscured from detection by the physical radar horizon�
Figure 7�2 shows that the three targets can be detected at the radar horizon for radar cross sections as low as −25 dBsm for the case of baseline radar sensitivity and a 0 dB propagation factor� The plot legend identifies the target altitudes� The detection range performance is for the case of a 0�9 probability of detection with 1 × 10−6 probability of false alarm� When the propagation factor increases to 20 dB, none of the targets are detectable at the radar horizon for radar cross sections below approximately −17 dBsm as shown in Figure 7�3� Sidelobe jamming can potentially reduce the target detection ranges shown in Figures 7�2 and 7�3�
The flyout performance for notional short-range (SR), medium-range (MR), and long-range (LR) air defense interceptors (ADIs) are summarized in Figure 7�4� Notional interceptor flyout times are plotted as a function of
the range of the target when intercepted� Average velocities for the notional interceptors were estimated based on the time to fly to their maximum range� Interceptor average velocities and notional minimum intercept ranges are summarized in Table 7�2�
The required target detection ranges for the SR, MR, and LR inter ceptor variants are shown in Figures 7�5 through 7�7, respectively, for the four firing doctrines considered include: Shoot (S), Shoot-Shoot (SS), Shoot-ShootShoot (SSS), and Shoot-Look-Shoot (SLS)� For higher speed targets, the required detection ranges can be beyond the horizon-limited radar detection ranges� The required detection ranges are interceptor dependent and include the system reaction, interceptor salvo, and look times as appropriate for the firing doctrine�
A battlespace performance chart as defined in this publication is a composite of some large but finite number of AMD system battlespace evaluation elements against singular, nonparametric, conditions� A notional battlespace
chart element is shown in Figure 7�8� Figure 7�8 is a graph of cumulative probability of track initiation (PDc) for the AMD system plotted against the target range to the defended asset� The radar PDc threshold is set to 90% (horizontal line) and the radar performance PDc is a function of target signature and altitude, AMD physical configuration, the environment, and radar settings� Vertical lines are a function of interceptor flyout time, target trajectory and Mach, weapon system doctrine, and time constant� The vertical line labeled as S indicates that a shoot opportunity is possible in this example�
To create a complete battlespace chart requires spanning the target set Mach and signature spread, altitude, and environmental requirements�
The overall performance of the AMD system for the three missile ADIs, three radar variants, and three propagation factor environments is summarized in Table 7�3� The target conditions are radially inbound speeds of Mach 1-3�5 at constant altitudes of 5, 10, and 50 m for nonfluctuating radar cross sections of 0 to −25 dBsm� The radar performance is best balanced to the ADI for the case of 12 dB additional radar sensitivity and a 20 dB propagation factor� Depth-of-fire performance is similar for the case of baseline radar sensitivity in a 0 dB propagation factor environment� Depth-of-fire performance is somewhat degraded for both the case of 12 dB additional radar sensitivity in a 40 dB propagation factor (overland engagement) environment and the case of baseline radar sensitivity and a 20 dB propagation factor�
The battlespace depth-of-fire results’ summary plots for baseline radar sensitivity with 0 dB propagation factor case are shown in Figures 7�9 through 7�17� A 0 dB propagation factor is representative of a very benign or best-case environment� The vertical boundaries between the different firing doctrines (e�g�, Shoot and Shoot-Shoot) indicate that the depth-of-fire performance is the same for targets with radar cross sections between 0 and −25 dBsm� This indicates that the radar has adequate sensitivity to detect the target when it crosses the physical radar horizon� These boundaries occur at different target speeds based on the performance variations between the SR,
MR, and LR ADIs� Comparing Figures 7�9 through 7�11, which summarize performance against the 5 m altitude target, we can see this variation in performance with interceptor type� The boundary between Shoot-Look-Shoot and Shoot-Shoot-Shoot is approximately Mach 2�1 for the SR interceptor, Mach 1�3 for the MR interceptor, and Mach 1�15 for the LR interceptor� This transition decreases in velocity with increased interceptor range capability� Increasing the minimum intercept range with interceptor velocity (see Table 7�2) is responsible for this trend� For the 10 m altitude target (see Figures 7�12 through 7�14), the maximum speed target that can be engaged with the Shoot-Look-Shoot doctrine improves for all three interceptors because the radar horizon has increased and the radar has adequate sensitivity to detect the target at or near the radar horizon (see Figure 7�2)� A similar trend can be observed for the 50 m target in Figures 7�15 through 7�17�
Similar depth-of-fire performance is achieved with 12 dB increased sensitivity radar in a 20 dB propagation factor environment as shown in Figures 7�18 through 7�20 for the case of the LR interceptor� Depth-of-fire performance is somewhat degraded for the higher target velocities and lowest radar cross sections� For these cases, the target is not detected immediately when it crosses the radar horizon due to insufficient radar sensitivity (see Figure 7�3)�
Overland scenarios are one of the more stressful environments for engaging low-altitude targets� Propagation factors can be very high� Propagation factors of 40 dB or higher are not uncommon in overland scenarios� Depth-offire performance for the case of 12 dB increased radar sensitivity with a 40 dB propagation factor is summarized in Figures 7�21 through 7�29� In this environment, the detection capabilities of the radar with 12 dB increased radar sensitivity are not adequate to detect some of the lower radar cross-section targets when they cross the radar horizon� This reduces the depth-of-fire performance for lower radar cross-section targets� Increased radar sensitivity and/or increased interceptor speed can be used to improve performance against the lower radar cross-section threats in an overland engagement environment�
In summary, the maximum target speed and minimum RCS capability, for the case of 12 dB increased radar sensitivity with a 40 dB propagation factor, are summarized in Table 7�4 for the Shoot-Look-Shoot firing doctrine� Table 7�4 breaks out the Shoot-Look-Shoot firing doctrine depth-of-fire performance by interceptor type and target altitude� In general, the short-range (SR) interceptor provides the best performance for low-altitude targets since the available engagement timeline is limited by the physical radar horizon and/or high propagation factors� In addition, the SR interceptor has the lowest minimum intercept range�
As the target height increases, the radar can detect the target sooner if it has adequate sensitivity� Earlier detection allows higher-speed targets to be engaged with a given interceptor� Table 7�4 shows how a target engineer can potentially defeat a weapon system by increasing target speed and/or lowering target RCS� The effectiveness of a weapon system improves with a layered defense approach� This allows the most effective weapon(s) to be selected based on the range and speed of the target at the time of radar detection�
After developing the answers to the questions how many and which interceptors can be delivered to the targets in question, it is necessary to answer
the question of single-shot probability of kill (Pssk)� Delivering an interceptor to a target does not necessarily mean that the interceptor can hit the target or achieve a sufficiently small miss distance against the target to cause enough damage to cause a mission kill� The interceptor must possess enough energy and a sufficiently small maneuver time constant to achieve adequately small miss distances to complete the engagement successfully� To conduct this analysis, a detailed end game, six-degree-of-freedom (6DOF) Monte Carlo miss distance simulation, is eventually required [3]� Within the preliminary design phase of development, it is reasonable and appropriate to conduct this analysis with a planar Monte Carlo-based terminal homing interceptor performance simulation, and as iterative passes provide more detailed definition of the design, it is possible to move to a true high-fidelity 6DOF� The planar simulation will include modeled seeker range-dependent and range-independent noise sources, radome boresight error, and possibly other Monte Carlo variables that will impact miss distance statistics�
Once the interceptor variants and the number of variants the system can deliver to the target is determined using the battlespace DOF analysis process, each of these interceptors is studied with planar simulations to assess miss distance performance� Figure 7�30 presents some of the results using a planar
Monte Carlo homing analysis tool� Figure 7�31 shows Monte Carlo miss distance results for one specific engagement and 250 runs� For this example, the engagement conditions included a 3-g target step maneuver, 0�001 rad of angle noise, and a −0�01 rad/rad radome boresight error slope� The interceptors’ zero degree angle-of-attack airframe characteristics are given in Table 7�5�
Monte Carlo results for a 10-and 9�5-second terminal homing time (THT) are shown in Figure 7�31 assuming that the interceptor is using true proportional navigation having a navigation constant of three and the measured states are estimated using a classic three-state Kalman filter� The plots on the right are histograms of miss distance probabilities� This is only an example; an actual
simulation may require more than 250 Monte Carlo runs to arrive at statistically meaningful results�
A summary chart can be constructed as a function of homing time to display the mean and standard deviation of the miss distance results� The example statistical miss distance set is provided in Figure 7�32 for homing times between 10 and 5�5 seconds� The results clearly indicate that homing times less than 6�5 seconds will require a significant increase in warhead capability or a kill strategy adjustment for the notional engagement and interceptor design tested�
Table 7�6 outlines a notional engagement preliminary design study with more stressing target requirements and additional noise sources including those errors introduced at handover� The 250 Monte Carlo run results are rolled up from each case� This evaluation set focuses on interceptor g-limit requirements as a function of handover error variations� All other error sources are held constant at nominal values�
Figure 7�33 shows results for one homing time condition, 7 seconds that include a parametric evaluation of interceptors having variable acceleration limits shown on the ordinate that correspond to Table 7�6� Two additional cases were added to include interceptor g-limits of 55 and 60 g’s�
Figure 7�33 shows the lethality miss distance threshold requirement to produce a 50% Pssk, which would be based on a lethality strategy that would have to be a flow-down requirement� According to this design study, the lateral acceleration limit of the interceptor as modeled would need to exceed 45 g’s assuming that 7 seconds is the minimal acceptable homing time� At this point, the preliminary design would proceed assuming that the airframe is capable of achieving this g-limit at the ranges necessary to satisfy the engagement boundary requirements�
A follow-on analysis shown in Figure 7�34 indicates that achieving a lethality ratio of one would require three interceptors on target to achieve the flow-down 0�9Pk requirement� A lethality ratio between 1 and 0�5 would be required to reduce the number of interceptors to 2� This would require a 50-g lateral acceleration capability interceptor according to Figure 7�33�
A preliminary design selection can be made once this analysis is completed for all interceptor design options against each target set and under the engagement considerations of interest� If this selection is to be based on, for example, target evasive maneuver level, then a selection chart like the one shown in Figure 7�35 would be developed� Several of these charts would be
required to examine interceptor design options where various target defense penetration features would be independently and in combination chosen as the independent variable�
Once the battlespace, DOF, and engagement analysis is completed, then a balanced set of AMD design options would be available either for moving into another iteration loop for preliminary design improvements or for moving to CDR� A traditional stoplight chart would be a mechanism to compile a massive amount of design and performance evaluation results into a succinct set of alternatives� Figure 7�36 shows an example of AMD down selection stoplight chart� Light gray corresponds to cases where requirements are partially met, gray corresponds to cases where requirements are met, and dark gray corresponds to cases where requirements are not met�
