Reading a Wind Turbine Like a Sine Graph
Track the height of a single turbine blade tip as it spins, and you get a perfect sine wave β amplitude, midline, period and all.
Introduction
A blade of length L on a hub of height h, turning at angular speed Ο, has a tip height y(t) = h + LΒ·sin(Οt + Ο) β the classic periodic-motion model, just applied to something more interesting than a Ferris wheel. With three blades 120Β° apart, you get three phase-shifted sine curves layered on top of each other. Push further and real turbines complicate the picture: they only hold a roughly constant RPM between "cut-in" and "rated" wind speed, idling below and feathering to a stop above β a genuine piecewise function riding on top of the sinusoid. There's also a strange bonus: film a spinning blade at the wrong frame rate and it can appear to freeze or spin backwards, the same "wagon-wheel" effect that shows up in old western films.
Guiding Questions
- How do you find the amplitude, midline and period of a single blade's height-versus-time graph from RPM, blade length and hub height?
- What do the three sine curves look like for a three-bladed turbine, and what's the phase offset between them?
- How would you model a turbine's RPM as a piecewise function of wind speed, including cut-in and cut-out?
- Why can a rotating blade appear to freeze or spin backwards on camera, and what does that tell you about sampling a continuous signal?
- Could you fit a real turbine's published power curve using the piecewise model you built?