A question was asked on how bad is the corner reflector structure in trying to design a low radar observable figher.
A: Really bad.
Actually, really really really really really really bad. Almost evil.
The primary rules for designing a low radar observable body are control of:
- Quantity of radiators
- Array of radiators
- Modes of radiation
The rules regarding the corner reflector are:
- Avoid the corner reflector
- If not possible, avoid the 90 deg type.
The corner reflector is a complex structure and as with any complex structure, there will be complex multi-facets reflections. Often it is said that if something is quantifiable and predictable, it can be controlled. While these reflections are mathematically quantifiable and predictable, aerodynamic necessities often prevent control methods. The most obvious corner reflector structure on any aircraft is the vertical-horizontal stabilators configuration and usually it is of the 90 deg type.
Consider the typical right angle, aka 90 deg, example below.
The structure can be broken down into discrete components, which for simplicity's sake, there are five. Upon radar bombardment each component becomes radiator R. Whether the structure is simulated measured or physically measured, the math of the interactions among radiators must be outlined.
For the above illustration...
The first example, in order of occurrence of radiation, could be 'R1R5' or 'R5R1'. Double edge diffractions.
The second example could be 'R2R4' or 'R4R2'. Double reflections.
The third example could be 'R5R1R3' or 'R3R1R5'. Double edge diffractions and single reflection. This example involves surface wave that travels from the single point of an edge diffraction to the corner of the two plates. Surface traveling waves have their own radiation patterns that will reflect off any nearby structure, but for simplicity's sake, those signals are not counted in this example.
The combinations of radiators interacting with each other will be compounded exponentially if the structure is rotated in a single axis, and even greater if the structure is in motion in 3D space, due to different angle of approaches to each component.
Knowing the order of occurrences is necessary. For example, if the radar threat is not going to affect the entire corner reflector structure, then perhaps absorber treatment is needed only at strategic locations instead of treatment for all the individual components. Another reason why is that different modes of radiation require different predictive/measurement techniques such as Physical Optics (PO) or Geometrical Optics (GO) or Methods of Moments (MOM). Knowning the exact characteristics of a particular signal may result in destructive interference which reduces contribution to final RCS.
This example does not factor in polarizations, whose signals will change upon reflection and/or diffraction, which will affect final RCS.
The complex interactions between corner reflector components are why missiles and bombs must be enclosed. A cluster of munitions is composed of many corner reflectors in close proximity with each other, making their contribution to final RCS the equivalent of holding a torch at night.
For the above example of a cluster of JDAM GBU30, each bomb have a tail assembly that contains 4 corner reflectors. Bomb no. 1 could be B1. The first corner reflector could be B1C1, then for the second corner reflector it would be B1C2, and so on. The naming convention must be uniform throughout the cluster. So for bomb no. 1 with the first corner reflector, a simplfied expression for an event that contains multiple diffractions and/or reflections could be: B1C1R2R4 or B1C1(R5R1R4R2) or B1(C1[R5R1R4R2]). Note the brackets and parentheses.
For bomb no.2 with the second corner reflector, one possible expression could be: B2(C2(R2R3R5R1)).
Because there is a cluster of corner reflectors, there would be an expression for interactions similar to this: B1(C1[B2(C2)]). This mean bomb 1 corner reflector 1 interacts with signals from bomb 2 corner reflector 2. There are no details of any signals from any radiator component (R) from any corner reflector. This is either an extremely coarse signal expression or a summary of interactions after all the radiator components have been factored. Not all corner reflectors faces each other so attention must be paid on how the individual bombs are arrayed in the cluster.
For the math and presumably at least one supercomputer that are being used to estimate the bomb cluster's own RCS, the more detailed (longer) the chain of radiators involved, the greater the precision of that estimation. There are no standardized expression formats simply because this is not a common thing to do in the industry. There are trade secrets, military secrets, and national security considerations in play. Diffraction points can be odd numbered 1, 3, 5, 7, and so on. Reflection surfaces or plates can be even numbered 2, 4, 6, 8, and so on. It is possible to even ignore the sources, which bomb and which corner reflector, of these signals and simply assign odd/even numbers to all known sources and go from there. But no matter the convention, whoever custom designed the math must be consistent and if a computer is used, the predictive/measurement software must be modified to use the custom math.
When the F-117 was under design, a computer with the performance of today's department store consumer personal computer was a luxury confined to engineering team leaders and project managers. RCS estimation of complex structures, from major flight control surfaces to access panel alignments to cockpit area, were done with long hand math much more complex and most engineers had their mechanical slide rulers.
Again...Keep in mind that this example is grossly simplified but even so, it already revealed the initial complexity produced by first-order reflections and first-order diffractions, not yet second- and third-, and certainly not a cluster of corner reflectors like in a bomb rack.
Currently, fighter designs need the vertical stabilator. Designs that have a single vertical stab will have the worst possible 'array of radiators' (rule 2) of the primary rules for designing a low radar observable body and of the secondary rules concerning corner reflectors in terms of contribution to final RCS. That is why for designs that must have the vertical stab for yaw axis stability and control, twin canted vertical stabs are used and they produce acute -- less than 90 deg -- angles with the rear horizontal stabs. Acute angles from canted vertical twin stabs greatly reduces the corner reflector's contribution to final RCS, but does not eliminate such contribution.
For the above F-22 profile, the rear horizontal stabs are not visible, but they are there. A single vertical stab produces two right angles. Twin canted vertical stabs produces three angles: two acute and one large obtuse. Initial assumption would be that since they are not right angles, the efforts to estimate their contribution to final RCS are not as important as right angles. This assumption is wrong.
Taken from the beginning of this explanation, two rules must be considered:
- Control of
QUANTITY of radiators.
- Avoid the corner reflector.
Twin canted vertical stabs do not so much 'violate' those rules as they are
LESS OBEDIENT to them.
An aircraft is a finite body that is also an assembly of many smaller finite bodies. A radar signal cannot stay on a finite body forever, hence there is the first-order diffraction signal off the edges of a finite body. Twin canted vertical stabs increases the quantity of radiators, which increases the level of first-order diffraction signals. A radar signal is not as straight as a simple arrow often used in illustrations, rather, a radar signal is a cone that expands in relation to distance, aka 'beam spreading'.
JetStream MAX - Doppler Radar Beams
The width of the beam expands at a rate of almost 1000 feet for every 10 miles of travel. At 30 miles from the radar, the beam is approximately 3,000 feet wide. At 60 miles, the beam is about 6,000 feet wide. At 120 miles the beam is nearly 12,000 feet or over two miles wide.
A weather radar beam is not designed/shaped/sharpened like a radar in a fighter jet but the core effect of beam spreading over distance is still the same. A radar beam is also
NOT unitary but instead composed of many lobes. A radar beam can be visualized/graphed and it would look like this...
The center/main lobe is where the seeking radar derive most of its information about the target. The side lobes are where corner reflectors with non-right angles can still contribute to final RCS. Their angles of approaches are different from the main lobe, hence they deserve their own first-, second-, and third- orders calculations and estimation. In other words, for a single corner reflector of
ANY angle, each lobe inside a radar beam warrant own investigation. Try to plug the main lobe somewhere into this expression: B1(C2(R2R3R5R1)). Do the same for all the other lobes. Then keep it uniform throughout the computer software. If there is no solid chain of communication between the design engineer and the measurement engineer, then the potential for an erroneous design increases.
This is why the first rule regarding the corner reflector is: Avoid the corner reflector. Twin canted vertical stabs are much more preferable than single vertical stab, but their physical attributes such as shape, dimensions, material, and arrangement have direct effects on their status as radiators and as such, they need equal diligence as the single vertical stab configuration. An obtuse (greater than 90) angle have the least RCS, an acute (less than 90) have slightly higher RCS, and the right (exactly 90) angle have the highest RCS.
The B-2 is of a flying wing design. The first generation flying wings, such as the Northrop YB-49, has vertical stabs for yaw axis stability and control. Because of advances in avionics, the B-2 is without the vertical stabs. So as far as major structures goes, the B-2 is the most obedient to the rule: Control of
QUANTITY of radiators. And that despite its size, its final RCS is so small that it threatens the efficacy of just about every air defense radars on the market.
In sum, the corner reflector is almost an evil in trying to design a radar low observable aircraft. It is aerodynamically necessary in many cases, such as the vertical/horizontal stabs arrangement, can be contained such as weapons enclosures, or hopefully avoided completely like with the B-2. Final note, this example is of a dihedral corner reflector typically found in major visual clues such as the vertical-horizontal stabs configuration. The trihedral corner reflector can be found on fuselage structure connection points. They may be much smaller than the vertical-horizontal stab configuration, but if allow to exist, to a seeking radar, they are are like flying with small lights.