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v0.9.1 · 2026-08-25
← Lesson MenuLesson 5b | Configuration
Redirect · Align · Shield

Low Observability (LO): Shape the aircraft's RADAR return.

Radar Cross Section (RCS) depends on wavelength, viewing angle, polarization, materials, and geometry. Early conceptual design cannot predict a final signature, but it can avoid shapes that strongly redirect incident energy toward the radar.

RADAR Range Equation

Explore how transmitter power, antenna gain, and aircraft radar cross section change a SAM radar’s idealized detection range.

SAM radar Red: idealized detection rangeRADAR SCOPE
Detection distance—Idealized Rmax
Aircraft range—
Radar statusSEARCH
Logarithmic: 1 kW to 10 MW
Logarithmic: 0.01 to 10 m²
Pr = PtGtGrσλ² / [(4π)³R⁴]

Teaching assumptions: Gt = Gr = G, λ = 0.03 m, and detection occurs when Pr ≥ 10−12 W. Propagation losses, clutter, jamming, atmospheric attenuation, and processing gain are omitted.

RF interference patterns

Observe how in-phase RF sources form constructive and destructive interference patterns.

Field Strength
Normalization
All elements radiate in phase: Δφ = 0°

Linear phased-array steering

A progressive phase change between neighboring elements tilts the combined wavefront and electronically steers the main beam without rotating the antenna.

Number of equally spaced transmitting elements.
Center-to-center element spacing in wavelengths.
Progressive phase applied from each element to the next.

Spacing is at the common λ/2 limit.

Orange: array-factor beam pattern · Blue: phase-aligned wavefronts
Steering angle14.5°Measured from array broadside
Phase progression−45°/elementNeighbor-to-neighbor phase delta
Visible-aperture length3.50 λ(N − 1)d
sin θ = −Δφ / [360°(d/λ)]

Aircraft Edges and Incoming-wave excitation

An edge is like an array fed by an incoming RADAR wave. An arriving wavefront reaches the edge elements at different times (and therefore phase angles); each element begins reradiating/reflecting the energy only when the front reaches its location. This is basically how reflection works (even on your mirror at home).

Measured from array broadside.
L/λ = 0 represents one element. Above that, element spacing is fixed at d/λ = 0.25.
Arrival condition at element i: s = xi sin θ
Incoming angle30°From broadside
First-to-last delay—Displayed in wave periods
Array stateIncident wave approachingAnimation repeats continuously
Blue: incoming wavefront and phase sine · Orange: reradiation and reflected beam

3D linear-array pattern

This solid rendering shows the normalized array factor in three dimensions. Drag the rendering to rotate it and inspect the main lobe, sidelobes, and any grating lobes.

3D planar-array pattern

Explore a rectangular planar array with physical length and width. Element counts are calculated automatically so adjacent elements remain spaced at one-quarter wavelength in both directions. A conducting backplane is positioned λ/4 behind the elements.

Total elements—Main-beam (-3dB)—Relative ERP—Broadside estimate; coherent elements with equal power per element.

Angled sides

A head-on low-observable shape uses canted sidewalls and tails to redirect side illumination away from the source.

Blue: incoming side illumination · Orange: reflected energy

Chines

A chine replaces a broad rounded leading surface with a sharp upper-body intersection. Reducing either principal radius reduces the estimated return from the double-curved surface.

Blue: incoming radar · Orange: specular reflections from each shape
Sphere σ—
Chined σ—
Flat-plate σ—
Double Curved Surfacesσ = πr1r2 / λ
Flat Plateσ = (4πA² / λ²) cos²θ sinc²(πL sinθ / λ)

Corner reflection

A two-surface corner redirects an incident wave through multiple specular reflections.

Blue: incoming wave · Orange: reflected return
Upper-face angle45°Relative to incoming wave
Lower-face angle45°Relative to incoming wave
Included corner angle90°Ideal retroreflection at 90°

Traveling waves over an aircraft skin

An RF wave produces an immediate reflection, while surface currents travel over the wing skin and excite a ringing response at the trailing edge.

Aileron Single incident wavefrontLocal leading-edge reflectionTrailing-edge radiation Reference diagram showing radar waves, traveling waves across a wing, and trailing-edge radiation

Planform edge shaping

Adjust the leading- and trailing-edge angles of the mirrored diamond fuselage and wings. The display combines them into one aircraft outline, so only exposed edges of the resulting planform generate patterns.

Aircraft Spikes
Fuselage Shading
Notional RCS “Bug Splat”Edge-only · 40 dB range0°270°180°90°Primary · Total Primary spikes: red · smaller reverse spikes: blue
Fuselage conditionDiamondLeft/right mirror symmetry
Number of spikes—Unique primary and reverse spike directions; directions within 3° are combined
θHPBW = 2 sin−1(2λ/L)   ·   σ = 10 log10(L²/π) dBsm
Calculated HPBW: —   ·   Edge σ range: —
Mirror-image beam power = ⅓ primary-beam power

The Bugsplat is an edge-only conceptual estimate. It does not model three-dimensional shaping, materials, cavities, diffraction, shadowing, or multiple scattering.

Inlet S-ducting

An S-shaped inlet hides the highly reflective engine face from direct radar line of sight. Drag the inlet and intermediate spline points to reshape the duct while the fan-face location remains fixed.

Blue → green → yellow → red: bounce sequence · Strength: line width
Initial strength100%Line width 10
Wall bounces—Before exit or cutoff
Returning strength—Relative to incident energy
Positive angles point downward on the display
Move the incident ray between the lower and upper inlet walls
0 = no absorption · 1 = complete absorption
After n wall reflections:
P/P0 = (1 − A)n
The fan face is modeled as a perpendicular, 100%-reflective surface.

Inlet scarfing

Reference drawings comparing inlet arrangements on the F-22, F-15, and F-106
Angles the left and right sides of the inlet lip
Angles the upper and lower sides of the inlet lip
Top
Side
Bottom
Orient surfaces

Tilt major facets so a specular reflection is directed away from likely illumination sectors.

Align edges

Use a small number of shared edge directions to concentrate returns into fewer angular sectors.

Manage cavities

Shield engine faces and avoid direct views into ducts, gaps, and other multiple-bounce features.

Preserve continuity

Blend joints and control discontinuities while respecting loads, volume, cooling, and maintainability.

Shapes that often increase return

  • Surfaces normal to the radar line of sight
  • Right-angle intersections and corner-like cavities
  • Direct views of compressor faces
  • Unaligned edges, gaps, antennas, and abrupt steps

Design consequences

  • Planform alignment may constrain sweep and control-surface layout
  • Shielded or curved ducts consume length, volume, and pressure recovery
  • Faceting and blending affect structure, internal volume, and aerodynamics
  • Doors, seals, apertures, coatings, and maintenance must be treated as a system