Units & conventions

VANE follows OpenFAST’s SI conventions on input and is explicit about the units it reports.

Quantities and units

Quantity	Unit	Notes
Rotor speed (input)	rad/s	As written in the .lin header (rotor_speed).
Rotor speed (reported)	rev/min	Campbell parameter rotor_speed_rpm = rad/s × 30/π.
Azimuth	rad (input)	Wrapped to [0, 360) deg internally for sweep checks.
Natural / damped frequency	Hz	natural_frequencies_hz, damped_frequencies_hz.
Angular frequency	rad/s	Used in theory expressions; ω = 2π f.
Damping ratio	dimensionless	ζ in [0, 1) for an underdamped mode.
Wind speed	m/s	Mean hub-height; 0 when InflowWind is absent.
Excitation harmonic	integer	The nP line, n × rpm / 60 Hz; n a positive integer.

Sign and normalisation conventions

• Eigenvalues: the conjugate representative with positive imaginary part is kept.

• Damping: ζ = -Re(λ)/|λ|; positive for a stable (decaying) mode. The solution separately counts unstable (positive-real-part) and over-damped (stable real) eigenvalues.

• Mode shapes: complex, phase-normalised so the dominant component is real and positive; correlations (MAC) are invariant to per-mode complex scaling, so the normalisation does not affect identification.

• Whirl direction: for the cyclic pair of a blade triplet, Im(q_s · conj(q_c)) > 0 is regressive (the lower-frequency w0 - Omega line) and < 0 is progressive, calibrated against the Coleman split (see Theory).

Confidence and uncertainty

Per-mode confidence is a dimensionless value in [0, 1] (1 = fully trusted). The azimuth-spread standard deviations are reported in the same units as the underlying quantity (Hz for frequency, dimensionless for damping).

Tabular export

vane.export writes the modal and Campbell tables with the column names and units above; the operating-parameter column is named after the diagram’s parameter (rotor_speed_rpm or wind_speed).