How do airplanes act as corner reflectors despite lacking significant flat surfaces in one of the three necessary mutually-perpendicular planes?

Question

One feature common to virtually all stealth aircraft is that they have vertical tails that are tilted away from actually being vertical (or lack them entirely). This is said to be because the 90° angles formed by, on the one hand, the vertical tail of a typical aircraft, and, on the other, its wing or horizontal stabiliser, act as corner reflectors, reflecting incoming radar signals back towards their source and giving other people a nice bright return from the aircraft; having a non-vertical vertical tail, or no vertical tail at all, eliminates this effect, scattering radio waves away from their source and drastically reducing the aircraft’s radar cross-section.

However, a corner reflector, in order to function as such, needs three mutually-perpendicular flat surfaces (shaped like the inside of a corner of a hollow cube, hence the name) in order to reverse an incoming photon’s motion in the x, y, and z axes and send it back towards its source. A reflector consisting of two perpendicular flat surfaces would reverse our photon’s motion in only two of the three spatial axes, sending it out on a track deflected 90° from its incoming trajectory, rather than the 180° necessary to return it to sender.

If we take an aircraft’s longitudinal axis (its roll axis, running from nose to tail) as its x axis, its vertical axis (its yaw axis, where you would stick a mounting pin through its fuselage¹) as its y axis, and its lateral axis (its pitch axis, running from wingtip to wingtip²) as its z axis, aircraft, even non-stealth ones, generally only have flat surfaces in (or near) the xy (vertical tail[s], opened landing-gear and bomb-bay doors) and xz (wings, horizontal tails, canards) planes, or in other planes at least reasonably close to parallel with the aircraft’s x axis; aircraft tend to avoid having large flat surfaces in the yz plane, as these would create impressive amounts of drag.

So where does the corner-reflector effect of a typical airplane come from?

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¹: Think of the airplane as a giant butterfly being mounted in a display box.

²: For aircraft with highly-swept wings (displacing the wingtips forward or aft), or where the amount of lift produced by the secondary horizontal surface (horizontal tail or canard) is a large fraction of that produced by the main wing (requiring the wings to be displaced away from the aircraft’s center of mass in order to keep its overall center of lift close to the center of mass), the lateral axis may not actually pass through the wingtips, but this serves as a pretty good approximation.

Answer 1

Generally airplanes have very little features that form perfect trihedral corner reflectors. As Niels explained in his answer, such features are not necessary for a plane with metal parts to be clearly visible on a radar.

However, very small features that act as trihedral corner reflectors do so very efficiently. Such features might be engine mounts, engine intakes/exhausts etc. Radar reflectors are commony used in sailing vessels, hence the link to the following article: Selecting a Radar Reflector , and a quote from it:

The effectiveness of an RTE is disproportionately related to its size. Assume that you have three theoretical reflectors of the same design, but of different sizes. Look at how rapidly the RCS (Radar Cross Section) increases with size. The RCS of a given reflector goes up by the fourth power of the radius, resulting in this dramatic increase in effectiveness.

The article continues to give following theoretical examples of RCS for certain radii of RTE's:

• 3" = 1.0m2
• 5" = 7.5m2
• 7" = 28.8m2

(Really don't understand why they mix imperial and metric units, but well...)

So: even a very small feature either acting as a trihedral corner reflector, or a dihedral corner reflector at a suitable agle will return a disproportionally large radar echo. Keep in mind that conventional aircraft fuselages have large areas where two curved surfaces blend, mainly the wing-body interface. Such areas create a sort of a three dimensional dihedral corner reflector that sweeps a large agle across space. These corner reflectors, though not trihedral, are very "visible" to radars.

The above is quite obviously the reason any trihedral features are avoided in stealth aircraft.

Now: it is unpractically hard to completely avoid features that act as dihedral corner reflectors in stealth aircraft. One such example is the F-117 Nighthawk, an ugly sob... Another, more aesthetic example is the B-2 bomber, which hardly is very maneuverable due to lack of efficient flight control surfaces. Modern stealth aircraft such as F-22 and F-35 accept some possible dihedral corner reflection spots, but mitigate the effect by use of non reflective / absorptive materials.

Epilogue: Modern civil radars do not need much of a return signal to spot a target, military radars even less so. The internet provides a plethora of comparisons (such as this) of RCS's of aircraft, generally ranging from the equivalent of an insect for F-22 and B-2, to the size of a car for the good old B-52. Be adviced that some modern military radar systems are able to target and track even the stealth aircraft from substantial distances (source will not be provided, dwi :)

Answer 2

A corner reflector is the most efficient way to generate a strong radar return from an incoming pulse. However, even if the plane has no corner reflectors in its overall structure, it will still generate a return because it is made of metal, and the characteristic impedance of the metal is sufficiently different from that of air to generate a reflection of the incoming electromagnetic wave. That reflection will not be collectively "aimed" straight back to the source is in the case of a corner reflector but if the incoming wave is strong enough and the radar receiver sensitive enough, the plane will still show up on the radar screen.