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Technology / Technical guide
Yaw Gear Ratios: Speed, Torque & Reflected Inertia
A gear ratio connects two rotational motions under a defined geometry. A speed reduction can increase the corresponding torque magnitude in an ideal lossless model, while changing how inertia is represented at either shaft. Those relationships do not create additional power.
Keep the input, output and ratio direction consistent.
A ratio is incomplete until its numerator and denominator are named. Speed, torque, angular displacement and reflected inertia can then be related within the same ideal model, rather than borrowing inverse ratios from different conventions.
01 / Ratio definition
State which speed is divided by which.
Here G = |ωin|/|ωout| is the input-to-output speed-magnitude ratio.
Here G = |ωin|/|ωout| is the input-to-output speed-magnitude ratio. A reduction has G greater than one. Tooth or pitch-radius relationships depend on the identified pair and arrangement. MathWorks describes gear constraints using explicitly named gears and geometric ratios.
Two directly meshing external gears rotate in opposite directions under parallel-shaft conventions. More complex trains can change that direction relationship. Using magnitudes for the scalar reduction does not erase the separate signed kinematic convention needed for a complete motion equation.
02 / Speed and angle
The motion ratio also relates displacement.
For a fixed ideal ratio, |ωout| = |ωin|/G.
For a fixed ideal ratio, |ωout| = |ωin|/G. The corresponding incremental angular displacements have the same magnitude ratio. Acceleration relations follow when the ratio and the chosen shaft directions remain fixed.
With a hypothetical G = 10 and input magnitude 2 rad/s, output magnitude is 0.2 rad/s. This is not an actual MARSTON yaw speed or reduction. A variable-ratio mechanism or compliance would require a different description from a rigid constant constraint.
03 / Torque and power
Ideal torque gain accompanies speed reduction.
For lossless steady transmission with compatible power directions, input and delivered output power magnitudes are equal: Tin|ωin| = Tout|ωout|.
For lossless steady transmission with compatible power directions, input and delivered output power magnitudes are equal: Tin|ωin| = Tout|ωout|. Thus Tout = G Tin. The torque gain is paired with reduced speed rather than multiplied power.
At the fictional ratio above, an input torque magnitude of 3 N m gives 30 N m at the output in that ideal balance. Real losses alter delivered power and the torque relation. A quoted ratio alone supplies no efficiency or actual available output torque.
04 / Reflected inertia
The nominated shaft sets the square factor.
For an output inertia Jout constrained by the same ideal ratio, kinetic energy is ½Jout ωout².
For an output inertia Jout constrained by the same ideal ratio, kinetic energy is ½Jout ωout². Rewriting it using ωin gives an equivalent input contribution Jin,ref = Jout/G². This is an energy-equivalent representation of the load, not a physical change in its mass.
Conversely, input inertia represented at the output contributes G²Jin. With invented Jout = 2 kg m² and G = 10, the input-referred value is 0.02 kg m². Both statements use this same ratio convention; silently reversing G would reverse the square factor.
05 / Real mechanisms
Ratio, backlash and holding are different properties.
Backlash describes a motion gap associated with the participating geometry; compliance describes deformation under force.
Backlash describes a motion gap associated with the participating geometry; compliance describes deformation under force. Neither is determined by the scalar ratio. Transient motion can consequently differ from the rigid ideal constraint even when the nominal tooth ratio remains unchanged.
Self-locking or holding behaviour also requires an identified mechanism and conditions. A large reduction does not automatically make a train unable to move from the output side. The relation Tout = G Tin is not a brake model or a holding-load certificate.
06 / Product scope
Generator direct drive does not define yaw transmission.
A generator and a yaw mechanism have different mechanical roles.
A generator and a yaw mechanism have different mechanical roles. A direct-drive generator statement concerns the rotor-to-generator path and cannot establish whether a separate yaw transmission uses gears. The physical boundaries remain distinct even on the same machine.
Electric yaw is confirmed across the current MARSTON range, and motor yaw is documented for FD14-50KW. No gear type, ratio, efficiency, backlash, inertia or holding function is assigned here. The explanation provides no gearbox selection, adjustment or operating command.
Related technical guides: Blade Centrifugal Loading & Rotational Prestress · Bolted Joint Stiffness: Load Sharing & Contact Separation · Bearing Internal Clearance, Preload & Elastic Contact.
General background: MathWorks: explicitly defined gear geometry and motion ratios. 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 |
|---|---|---|
| Ratio convention | G = |ωin|/|ωout| | Numerator and denominator are named. |
| Output speed | |ωin|/G | Fixed ideal reduction magnitude. |
| Ideal output torque | G Tin | Lossless compatible power balance. |
| Load at input | Jout/G² | Energy-equivalent inertia contribution. |
| Input at output | G²Jin | Same ratio convention, opposite reference shaft. |
Engineering questions.
Does reduction create extra power?
No. The ideal torque increase accompanies a speed decrease.
Do all gear trains reverse direction once?
No. Signed motion depends on the arrangement.
Is reflected inertia a changed physical mass?
No. It is an equivalent representation at a nominated shaft.
Which inertia factor applies at the input?
For G = input speed/output speed, the output load contributes Jout/G².
Does a large ratio guarantee holding or self-locking?
No. Those properties require the actual mechanism and conditions.
Does FD14-50KW direct drive identify its yaw ratio?
No. Generator drive and yaw transmission are different mechanical paths.
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