Wind Noise Physics

Investigating and confirming the physics behind cycling ear-wind noise...

Wind Tunnel Testing Baseline: ~17.5 mph mean wind speed with ~2.5% turbulence intensity.

(Velocity pressure: 37.5 Pa = .5*1.225 kg/m^3*(7.8232 m/s)^2

The pressure fluctuations within the concha cavity, the bowl-shaped area just outside the ear canal opening, are a very good approximation of the pressure fluctuations experienced by the eardrum. This is because the ear canal, while having its own resonant characteristics, is a relatively short and direct pathway from the concha. Therefore, pressure waves entering the concha propagate quickly and with minimal attenuation or distortion to the eardrum. While subtle differences might exist due to the ear canal's specific geometry, for most practical purposes, particularly when considering broader frequency ranges like those involved in wind noise, the pressure variations in the concha can be considered representative of those acting on the eardrum. This simplifies measurement, as placing a microphone in the concha is often easier and less invasive than placing it deep within the ear canal.

Verified: Extech 755 Differential Manometer with 180 degree head rotation (some slight <2 Pascal variation).

The "-5/3 law" itself describes the spectral content of the turbulent kinetic energy. Since pressure fluctuations are a direct consequence of the turbulent velocity fluctuations, their spectrum is related to this -5/3 law, though not identical.

* Turbulent Kinetic Energy Spectrum: The "-5/3 law," formally part of Kolmogorov's theory, describes how kinetic energy is distributed across different scales (or frequencies) of turbulent eddies. It states that the energy E(k) at a given wavenumber k (related to eddy size) is proportional to k^(-5/3). This is the energy spectrum of the turbulence.

* Relationship to Pressure Fluctuations: The pressure fluctuations that cause wind noise are generated by the turbulent eddies. Larger eddies tend to produce lower-frequency pressure fluctuations, while smaller eddies produce higher-frequency fluctuations. There's a connection between the velocity fluctuations (described by the -5/3 law) and the resulting pressure fluctuations.

* Pressure Spectrum: The pressure spectrum describes how the energy of the pressure fluctuations is distributed across different frequencies. While it's related to the turbulent kinetic energy spectrum, it's not exactly the same. The relationship is complex and depends on factors like the specific geometry of the ear and how the turbulent flow interacts with it.

* Similar Trend: In general, you'll see a similar trend in the pressure spectrum as in the turbulent kinetic energy spectrum. There will be more energy at lower frequencies (corresponding to larger eddies) and less energy at higher frequencies (smaller eddies). However, the exact power law and the detailed shape of the pressure spectrum can be modified by the factors mentioned above.

* Importance of Measurement: To get the actual pressure spectrum of cycling wind noise, you need to measure the pressure fluctuations at the ear using a sensitive microphone. While the -5/3 law provides a general idea of the trend, it won't give you the precise details of the pressure spectrum at the eardrum.

In summary, the "-5/3 power law" describes the energy spectrum of the turbulent kinetic energy. The pressure spectrum of cycling wind noise is related to this, showing a similar trend of decreasing energy with increasing frequency, but it's not identical. Direct measurement is needed to determine the precise spectral content of the wind noise at the ear.

The tragus, that little flap of cartilage in front of the ear canal, plays a surprisingly significant role in generating the turbulence that ultimately causes the eardrum to vibrate and produce wind noise. Here's a step-by-step breakdown of the physics involved:

* Flow Separation at the Tragus: As wind flows past the head, it encounters the tragus as an obstacle. This causes the smooth flow of air to separate from the surface of the tragus. Flow separation is a phenomenon where the boundary layer (the thin layer of slower-moving air near the surface) detaches from the surface.

* Vortex Formation: This flow separation leads to the formation of vortices – swirling regions of air – in the wake of the tragus. These vortices are essentially pockets of rotating air with lower pressure than the surrounding flow.

* Turbulence Amplification: The vortices shed from the tragus contribute to the overall turbulence of the flow over the concha. They interact with the larger-scale turbulent structures in the wind, creating a complex and chaotic pressure field.

* Pressure Fluctuations in the Concha: This amplified turbulence generates pressure fluctuations in the concha cavity, the bowl-shaped area just outside the ear canal. These pressure fluctuations are not just random; they contain a range of frequencies related to the sizes and rotation speeds of the vortices and other turbulent structures.

* Ear Canal as a Conduit: As we discussed earlier, the ear canal acts as an efficient conduit for transmitting pressure fluctuations from the concha to the eardrum. The short length and relatively wide diameter of the canal mean that pressure waves travel through it quickly and with minimal attenuation.

* Eardrum Vibration: The pressure fluctuations impinging on the eardrum cause it to vibrate. The eardrum is a thin membrane that's very sensitive to pressure changes. It vibrates in response to the fluctuating pressure field, even if the frequencies are outside the audible range.

* Perception of Wind Noise: The vibration of the eardrum is what we perceive as wind noise. The specific characteristics of the noise (its loudness, pitch, and timbre) depend on the frequency content and intensity of the pressure fluctuations, which are influenced by the turbulence generated by the tragus and the overall flow field.

In summary:
The tragus, by causing flow separation and vortex formation, acts as a turbulence amplifier. This turbulence generates pressure fluctuations in the concha, which are then transmitted to the eardrum, causing it to vibrate and produce the sensation of wind noise. Understanding this process highlights the importance of the tragus in the generation of cycling wind noise and emphasizes the potential for products like Cat-Ears to disrupt this flow and reduce the noise.