As discussed in subpar. 2-3.1.1, parts of the guidance sys- tems of some missiles are located on the ground. Flight sim- ulations for missiles that have ground-based guidance are essentially the same as flight simulations for missiles that have airborne guidance except that in some cases steering commands are directed to the autopilot from the ground
instead of from a seeker and different guidance laws may be employed.
8-2.4.1 Semiactive Homing
A surface-to-air, semiactive homing system (subpar. 2- 3.1.2.2) requires a target illuminator on the ground. The seeker on the missile tracks the power reflected from the tar- get in the same way as a passive homing system. Except for considerations of signal strengths and Doppler effects, which are outside the scope of this handbook, simulating the flight of missiles that employ semiactive horning is the same as simulating the flight of missiles that employ active or passive homing.
8-2.4.2 Command
The simulation of command guidance depends on the particular guidance law employed. If proportional naviga- tion is used by the command system, ground-based comput- ers-combined with ground-based target and missile trackers-determine the line-of-sight vector from the mis- sile to the target and calculate the angular rate wÓ. ThiS
angular rate is then processed in the ground computer through an equation such as Eq. 8-8 to determine the com- manded-maneuver-acceleration vector Ac, which is trans- mitted to the missile. The missile autopilot then determines and distributes control-surface deflection commands to the control system. A missile flight simulation for a missile that employs command proportional navigation uses the same equations that are used for proportional navigation in a homing system except, of course, that missile seeker track- ing is not simulated.
8-2.4.3 Beam Rider and Command to Line of Sight
Command-to-line-of-sight guidance is similar to beam- rider guidance, in that both forms attempt to keep the mis- sile within a guidance beam transmitted from the ground.
Normally, the guidance beam is aligned with the line of sight from the ground-based target tracker to the target. In some systems, ‘however, the guidance beam does not always point directly toward the target it may be biased forward during the midcourse portion of the engagement to provide a lead angle. In beam-rider guidance the error in the position of the missile relative to the center of the guidance beam is detected by sensors onboard the missile (subpar. 2-3.2.3), and maneuver commands to correct the error are determined onboard. In command-to-line-of-sight guidance the missile position error is detected by sensors on the ground, and guidance maneuver commands are transmitted to the mis- sile from system elements on the ground (subpar. 2-3.1.1.3).
The basic equations for missile flight simulations that use these two types of guidance are identical.
As shown in Fig. 8-10, the vector e represents the error in missile position relative to the guidance beam at any given
instant. This error is defined as the perpendicular distance from the missile to the centerline of the guidance beam. The missile guidance commands generated by beam-rider and command-to-line-of-sight systems are proportional to the error vector e and the rate of change of that vector . The proportionality with e causes the missile to be steered toward the center of the guidance beam; the proportionality with provides rate feedback, which causes the missile flight path to maneuver smoothly onto the centerline of the guidance beam without large overshoots.
A third parameter, the Coriolis acceleration ACC, maY be included in the guidance equation. This Coriolis accelera- tion results from the angular rotation of the guidance beam and should not be confused with the Coriolis effects caused by the rotation of the earth. The Coriolis component of mis- sile acceleration is required in order to allow the missile to keep up with the rotating beam as the missile fries out along the beam. In surface-to-air missile applications the angular rate of the guidance beam is typically great enough to cause this parameter to be significant. If the Coriolis term is not included, the rnissile position lags behind the rotating guid- ance beam, which results in increased miss distance. This Coriolis acceleration term is included in the guidance loop as a feed-forward term, i.e., it is not affected by feedback loops.
Equations for calculating the guidance parameters e, and ACC are presented in this paragraph, the method of com- bining them to form the missile commanded-lateral-acceler- ation vector AC is given by Eq. 8-21.
For convenience in demonstrating the method of calculat- ing the error vector e, assume the guidance beam transmitter (which may be identical to the target tracker) is located at the origin of the earth coordinate system. Define a unit vec- tor ugl to represent the direction of the guideline, i.e., the centerline of the guidance beam. The error vector e is per- pendicular to ugl. The equation for calculating e is
The vector PB, for use in Eq. 8-16, determines the loca- tion of the intersection of the guideline and the error vector e;t is calculated by
8-14
Figure 8-10. Guidance Error for Beam Rider or Command to Line of Sight
The Coriolis acceleration term ACc is calculated using
The dot product in Eq. 8-20 gives the component of missile velocity along the guideline; thus the term in square brack- ets is one-half the Coriolis acceleration vector.
Finally, using the terms calculated in Eqs. 8-16,8-18, and 8-20, the commanded-lateral-acceleration vector, to guide the missile onto the centerline of the guide beam, is given by
The missile lateral acceleration commands are con- strained to be in directions perpendicular to the missile cen- terline. The unit vectors ue, , and uC, for use in Eq. 8-21, are defined to meet this constraint by
In five-or six-degree-of-freedom simulations the missile commanded-lateral-acceleration vector AC is transformed into the missile body coordinate system and substituted into Eq. 8-14 or 8-15 to calculate control-surface deflections. In three-degree-of-freedom simulations AC is substituted directly into Eq. 7-18 to calculate the achieved lateral accel- eration of the missile.
All of the parameters used in the simulation to calculate the missile acceleration command (Eq. 8-21) may not be available to the guidance system of an actual beam-rider or command-to-line-of-sight missile. Therefore; care must be taken to distinguish which parameters in the simulation are simply representations of the physics of the engagement and which can actually be known within the missile guidance system of the particular missile system being simulated. For example, the missile velocity VM, required to determine the Coriolis acceleration term ACc may not be known accurately onboard a beam-rider missile. In this case it may be neces- sary to use an approximate value within the actual guidance system in order to take advantage of the Coriolis feed-for- ward term. The approximate value should, of course, also be employed in the simulation.
8-2.4.4 Track Via Missile
In track-via-missile guidance relative target position and rate measurements are made onboard the missile and trans- mitted to the ground computer for processing. Maneuver 8-16
acceleration commands are transmitted back to the missile, which executes the maneuver. Assuming that proportional navigation is the guidance law employed, track-via-missile guidance modeling for a missile flight simulation is the same as the modeling described for homing guidance in subpars. 8-2.1,8-2.2, and 8-2.3.