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Technology / Technical guide
Yawed Rotor Inflow: Velocity Components & Skewed Wake
Yawed inflow makes the wind direction differ from the rotor-axis direction. Resolving the flow into normal and in-plane components is only the first step. The rotating sections and induced wake can then encounter an asymmetric aerodynamic state.
Follow the geometry before discussing the response.
A signed yaw angle needs an axis and direction convention. Projection explains the incoming components, while the wake and local blade loading require additional aerodynamic relationships beyond the geometric angle alone.
01 / Geometry
A yaw angle describes an orientation relationship.
For the simple horizontal geometry used here, γ is the signed angle between the rotor axis and the nominated incoming velocity direction.
For the simple horizontal geometry used here, γ is the signed angle between the rotor axis and the nominated incoming velocity direction. The axis normal to the rotor disk and the velocity reference must be defined together. Tilt and structural motion add distinctions outside this two-dimensional illustration.
A meteorological wind-from heading uses a different directional convention from a velocity pointing toward the direction of flow. Those descriptions cannot be subtracted as if identical. The direction-and-alignment guide explains that prior reference question.
02 / Projection
One vector produces normal and cross-flow components.
For a uniform horizontal velocity of magnitude U in this defined geometry, the disk-normal component is U cos γ and the in-plane cross-flow component is U sin γ.
For a uniform horizontal velocity of magnitude U in this defined geometry, the disk-normal component is U cos γ and the in-plane cross-flow component is U sin γ. These are vector projections; they do not by themselves state induced velocity or electrical power.
With hypothetical U = 10 m/s and γ = 30°, their magnitudes are about 8.66 and 5 m/s. Reversing γ changes the cross-flow sign while retaining the same cosine projection. A sign reversal can therefore reverse a spatial asymmetry without changing that normal-speed magnitude.
03 / Azimuth
Rotation changes how cross-flow meets a section.
A blade section’s tangential direction changes around the rotor.
A blade section’s tangential direction changes around the rotor. The fixed cross-flow component consequently projects differently onto that local direction at different azimuths. Relative flow includes the section motion as well as the surrounding air velocity.
This can introduce periodic variation in a section’s flow angle and speed even when the nominated upstream wind vector is steady. It is distinct from a gust changing the entire upstream wind in time. No actual MARSTON angle-of-attack history follows from this geometric explanation alone.
04 / Wake response
The induced field need not remain axisymmetric.
A loaded rotor changes flow momentum, and yawed conditions can produce a skewed or deflected wake with a nonuniform induced field.
A loaded rotor changes flow momentum, and yawed conditions can produce a skewed or deflected wake with a nonuniform induced field. FAST.Farm theory separately describes wake-plane deflection and a curled-wake representation for skewed inflow.
These are model distinctions, not proof that every wake has one prescribed shape. Wake direction, rotor-axis direction and far-upstream velocity direction should not be declared identical. Their relationship also depends on loading and the surrounding flow represented by the chosen model.
05 / Power shortcuts
A normal projection is not a complete yaw-loss law.
Cubing U cos γ in a simplified energy expression would produce a cosine-cubed factor only within its associated assumptions.
Cubing U cos γ in a simplified energy expression would produce a cosine-cubed factor only within its associated assumptions. That manipulation cannot establish a universal measured yaw-loss exponent for a real rotor, much less for a complete electrical package.
Local coefficients, induction, rotational motion and operating response remain relevant. A model that compresses these effects into one fitted factor needs its own conditions. This page explains why the geometric projection and the resulting machine power are different levels of description.
06 / Conditions
Separate aerodynamic explanation from yaw commands.
A blade-element model may require an explicit skewed-flow treatment; a more detailed wake representation has different assumptions and computational scope.
A blade-element model may require an explicit skewed-flow treatment; a more detailed wake representation has different assumptions and computational scope. Increased model detail alone does not certify a load or performance prediction. The BEM guide covers the underlying coupling.
Electric yaw is confirmed for the current MARSTON range, but no yaw-loss exponent, wake-steering function or implemented correction algorithm is assigned here. This explanation provides no intentional misalignment setting, manoeuvre schedule or operational adjustment.
Related technical guides: Wind Turbine Dynamic Pressure, Static Pressure & Coefficients · Wind Turbulence Spectra, Time Scales & Spatial Scales · Rotor Spatial Averaging: Point Wind, Area Mean & Equivalent Speed.
General background: OpenFAST FAST.Farm: yaw reference, wake deflection and skewed-flow models. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Yaw angle | γ with defined axes and sign | Velocity direction and wind-from heading differ. |
| Normal component | U cos γ | Simple uniform horizontal projection. |
| Cross-flow component | U sin γ | Sign changes with the yaw convention. |
| Azimuthal variation | Local rotating-section projection | Can occur under steady upstream flow. |
| Skewed wake | Induced-flow model response | Not specified by projection alone. |
Engineering questions.
Does yawed inflow contain only a lower normal speed?
No. It also has an in-plane component in the stated geometry.
Does reversing yaw sign change U cos γ?
Its magnitude is unchanged, while the sine component reverses.
Can a steady yawed wind create periodic section variation?
Yes. The section’s direction changes as it rotates.
Must wake direction equal rotor-axis direction?
No. A loaded, skewed flow can deflect and remain nonuniform.
Is cosine cubed a universal real-turbine yaw-loss law?
No. It follows from a particular simplification, not every machine response.
Does electric yaw confirm wake steering?
No. An aerodynamic concept does not establish that control function.
Technical enquiry
Discuss the technical question.
Yawed inflow makes the wind direction differ from the rotor-axis direction. Share the model and applicable operating or design information for an engineering discussion.