Vessel wake analysis for speed and heading reconstruction
High-resolution SAR and optical imagery preserve the geometry of a vessel's Kelvin wake long after the ship has moved on, allowing analysts to reconstruct speed, heading, and manoeuvre history independent of AIS. Resolution better than 3 m GSD is the practical threshold for reliable extraction.
Sensors
- Capella Space SAR (X-band): Spotlight mode delivers approximately 0.5 m GSD, well below the 3 m threshold needed for wake geometry extraction. Rapid retasking supports near-real-time collection on specific vessels of interest. X-band backscatter responds strongly to the capillary-wave suppression in the turbulent wake centreline.
- ICEYE SAR (X-band): Spot Extended mode achieves approximately 0.5 m range resolution. ICEYE's large constellation (over 30 satellites as of 2024) offers revisit intervals under one hour over many ocean areas, which matters when a vessel is manoeuvring and wake geometry is changing rapidly.
- Maxar WorldView-3 (optical, panchromatic): 0.31 m native panchromatic GSD makes wake arms visible in moderate sea states. Optical collection is cloud-limited and requires low sun glint angles to reveal the surface-roughness contrast of the wake. Useful for colour confirmation of hull type alongside wake geometry.
- Airbus Pléiades Neo (optical, panchromatic): 0.30 m panchromatic GSD with daily revisit over most ocean areas. Like WorldView-3, it is cloud-dependent, but the sub-metre resolution resolves both the diverging Kelvin arms and the narrower turbulent centreline in calm-to-moderate conditions.
What the 19.47-degree angle actually tells you
Lord Kelvin proved in 1887 that the half-angle of a ship's wake envelope is a universal constant: 19.47 degrees, independent of vessel speed, provided the water is deep relative to the wavelength of the surface waves generated. This geometry is preserved in satellite imagery long after the vessel has passed. Measuring the angular width of the two diverging wave arms in a SAR or optical image gives an immediate confirmation that what you are looking at is a ship wake and not a current boundary or bathymetric feature.
Speed is not read from the envelope angle, which is constant, but from the spatial wavelength of the transverse and diverging wave components within the arms. The ratio of wavelength to the known gravitational dispersion relation for surface gravity waves yields vessel speed. In practice, analysts measure the dominant wave crest spacing in the diverging arms and apply the deep-water dispersion relation (phase speed proportional to the square root of wavelength times g over 2π). Published studies using ERS-1 and later Sentinel-1 data have demonstrated speed retrieval accuracy of roughly plus or minus one to two knots under favourable sea-state conditions, though this degrades in high seas.
SAR versus optical: different physics, complementary limits
SAR detects wakes through changes in surface roughness. The turbulent centreline suppresses short capillary waves, reducing backscatter and appearing as a dark stripe. The Kelvin arms, by contrast, can appear bright or dark depending on the look angle and the local wave slope relative to the radar beam. X-band SAR (wavelength around 3 cm, used by Capella and ICEYE) is particularly sensitive to centimetre-scale capillary waves, making it well suited to turbulent wake detection even under overcast skies. The wake centreline can remain detectable for several kilometres behind a large vessel in calm water.
Optical imagery detects the same roughness contrast but requires adequate sun-glint geometry. At low glint angles, the wake arms appear as brightness variations against the background ocean. The advantage is colour information and the ability to see vessel hull details simultaneously. The hard limit is cloud cover, which is irrelevant to SAR. For a vessel that has disabled AIS and is operating in a cloud-prone region, SAR is the primary tool. Optical imagery is most useful for corroboration and for extracting hull-type context that SAR alone cannot provide.
One honest caveat: in sea states above Beaufort 4 or 5, background wave clutter begins to obscure the Kelvin arm geometry in both sensor types. Turbulent centreline detection is more resilient but still degrades. Strong ocean stratification can also shift the effective wake angle away from the theoretical 19.47 degrees if internal wave generation dominates, which introduces ambiguity in speed estimates.
Reconstructing a manoeuvre history from a single pass
A satellite makes one pass. The vessel has moved on. But the wake is a time-stamped record written on the water. Because surface gravity waves propagate away from the ship's track at predictable speeds, the distance behind the vessel at which a given wave crest appears encodes how long ago that crest was generated. A course change produces a visible kink in the wake centreline. The angular difference between the old and new centreline segments gives the turn magnitude; the distance of the kink behind the vessel's current position, divided by the estimated vessel speed, gives the approximate time of the manoeuvre.
This method is not forensically precise. Wake persistence depends on sea state, wind speed, and the density stratification of the upper ocean, all of which vary. In calm conditions, a large vessel's turbulent wake can persist for 30 minutes or more and extend for many kilometres. In rough conditions, the same wake may be undetectable after five minutes. Analysts must treat manoeuvre-history reconstructions as probabilistic bounds, not exact logs. When combined with AIS gaps and known port schedules, even an approximate reconstruction significantly narrows the uncertainty about where a vessel has been.
Doppler shift as a cross-check on wake-derived speed
Stripmap and spotlight SAR modes record a Doppler frequency shift for targets moving relative to the sensor. A vessel moving toward or away from the satellite's ground track introduces a measurable azimuth displacement in the focused image, proportional to its radial velocity component. This is a separate measurement from wake geometry and provides an independent estimate of the vessel's speed projected onto the radar's look direction.
Combining Doppler-derived radial speed with wake-derived total speed resolves the heading ambiguity that either method alone leaves open. Wake geometry gives speed magnitude and a heading axis but cannot distinguish between the two opposite directions along that axis without additional context. Doppler shift resolves the ambiguity because it has a sign. The two methods are therefore complementary: wake geometry provides the kinematic history and heading axis; Doppler provides the directional sense and an independent speed check. Where they agree, confidence is high. Where they disagree, the image merits closer scrutiny for multi-vessel scenes or unusual sea-state effects.
Resolution floors, archive depth, and what you cannot recover
The 3 m GSD threshold is a practical rule of thumb drawn from published SAR wake-detection studies. Below that resolution, the transverse wave crests within the Kelvin arms are undersampled and wavelength measurement becomes unreliable. Sentinel-1 IW mode at 10 m GSD can detect the presence of a wake and give a rough heading, but speed retrieval from wave-crest spacing is not dependable at that resolution. Commercial SAR at sub-metre resolution is genuinely necessary for quantitative speed extraction.
Archive depth is a real asset. Capella, ICEYE, and the commercial optical constellations have been collecting since 2018 to 2020, and historical tasking archives for specific areas of interest can extend further through Maxar's legacy WorldView-1 and WorldView-2 holdings. Reconstructing a vessel's pattern of behaviour over months requires systematic archive queries rather than single-event collection. Satellize runs wake-geometry extraction as part of broader dark-vessel analytics pipelines, with the same open-constellation and commercial-tasking architecture it uses in programmes such as the Tonga crop-estimation work, adapted here to maritime geometry rather than agricultural spectral indices.
What you cannot recover: if no satellite passed during or shortly after a manoeuvre, there is no wake to analyse. Wakes do not persist long enough to bridge gaps of more than an hour in most sea conditions. This is why revisit rate matters as much as resolution, and why multi-constellation access, combining Capella and ICEYE passes with opportunistic optical collection, is the operational standard for serious maritime intelligence work.
Typical figures
| Minimum useful GSD for speed extraction | Better than 3 m; sub-1 m preferred (Capella/ICEYE spotlight: ~0.5 m) |
| Kelvin wake half-angle (deep water) | 19.47 degrees (universal constant for deep-water surface gravity waves) |
| Speed retrieval accuracy (SAR, calm seas) | Approximately ±1–2 knots under Beaufort 3 or below; degrades above Beaufort 4 |
| Wake persistence (turbulent centreline) | 5–30+ minutes depending on sea state, wind, and stratification |
| SAR frequency (primary sensors) | X-band (~9.6 GHz, ~3 cm wavelength) for Capella and ICEYE |
| Optical panchromatic GSD (best available) | 0.30–0.31 m (Pléiades Neo, WorldView-3) |
| Revisit interval (multi-sensor combined) | Under 1 hour over priority areas with Capella + ICEYE combined tasking |
| Archive depth (commercial SAR) | Capella from ~2020, ICEYE from ~2018; Maxar optical from 2007 (WorldView-1) |
| Cloud sensitivity | SAR: cloud-transparent. Optical: blocked by cloud cover; glint geometry required |
| Minimum vessel size for wake detection | Approximately 50 m LOA in calm conditions at sub-1 m GSD; larger vessels in higher sea states |
Analytics Satellize can run
| Vessel speed estimate from Kelvin arm wavelength | Deep-water dispersion relation applied to dominant crest spacing measured in diverging wake arms | Speed value with uncertainty band (knots), delivered as attribute in vessel event report |
| True heading reconstruction | Kelvin envelope bisector geometry combined with Doppler azimuth displacement for directional disambiguation | Heading bearing (degrees true) with confidence flag, GIS point feature |
| Manoeuvre history log from wake centreline kink analysis | Centreline digitisation and kink-angle measurement with time-offset estimation from wave propagation distance | Timestamped manoeuvre sequence (turn bearing, approximate time of turn), PDF report or GeoJSON track |
| AIS-gap kinematic fill | Wake-derived speed and heading inserted into AIS position gap to generate a probable track segment | Interpolated track GeoJSON with provenance flag distinguishing AIS-reported from wake-inferred positions |
| Multi-pass behavioural pattern assessment | Archive query across Capella, ICEYE, and optical holdings; wake geometry extracted per pass and aggregated | Vessel behaviour summary over analyst-defined time window, tabular report with supporting image chips |
| Sea-state quality flag for wake retrievals | ERA5 reanalysis wind and wave fields co-registered to image acquisition time and location | Per-image confidence tier (high/medium/low) appended to all wake-derived speed and heading outputs |
Who does the work
We can get this done for you. Satellize runs its own analyst desk and a strong science team. You do not buy a data feed and work out what it means; our people source the imagery, run the analysis described on this page, and hand you the answer with its confidence limits stated. Discuss this requirement.