Presets
Playback
Wind, air and sensor
Each path sends pulses both ways. The wind adds to the sound speed one way and subtracts the other way, so the two transit times differ in proportion to the wind component along the path.
Model checks
The science
What is modelled
Two perpendicular acoustic paths of length L. A pulse travels each path in both directions; the wind component along the path shifts the two transit times, and the instrument turns the pair into a velocity. The wind has a steady part and an Ornstein-Uhlenbeck gust.
Equations
- Speed of sound
c = 331.3 sqrt((273.15 + T)/273.15) + 0.0124 RH. - Transit times
t1 = L/(c + v),t2 = L/(c - v). - Inversion
v = (L/2)(1/t1 - 1/t2); time differencet2 - t1 = 2 L v / (c^2 - v^2). - Noise
sigma_v = J sqrt((c+v)^4 + (c-v)^4) / 2Lfor timing jitter J.
Checks run in the page
- Speed of sound against the ideal-gas value.
- Exact inversion of ideal transit times.
- Transit-time difference formula.
- Monte Carlo scatter against the error-propagation formula.
Honest simplifications
An illustrative model: the humidity term is a linear fit, there is no flow distortion by the transducer heads, no temperature gradient along the path and no crosswind correction. Not a calibrated instrument.
What to try
- Press Noisy clock and watch the measured arrow wobble even though the true wind is steady.
- Raise the path length: the same jitter then produces less velocity noise.
- Press Frozen calm: the speed of sound drops and the transit times grow.