Calculations

Calculating wind noise reduction can be confusing because it involves both a logarithmic scale and a frequency-weighted measurement that mimics human hearing. This page details the methodologies used to quantify noise reduction, focusing on how decibel measurements, particularly dB(A), are converted into meaningful percentage values. We will cover the calculations that underpin these metrics, providing clarity on the difference between a percentage reduction in sound pressure and a percentage reduction as perceived by the human ear.

Cycling ear-wind noise is primarily comprised of pseudo sound and dipole acoustic sound:

Pseudo-Sound: This refers to the direct, non-propagating pressure variations within the turbulent airflow immediately surrounding and impinging upon the ear canal opening. Think of it as the chaotic "whooshing" sensation you feel and hear directly on your ear. As we've noted, pseudo sound is hydrodynamic.

Dipole Acoustic Sound: As airflow separates and sheds vortices from various parts of the cyclist's head and helmet (e.g., ear, helmet edges, straps), these unsteady fluid-structure interactions can generate propagating acoustic waves. These are sound waves that travel to your eardrum. As we've noted, dipole is acoustic.

A microphone, placed correctly in the ear canal, can accurately capture both of these sources.

Microphones

Professional ultra-high-sensitivity microphones
In the canal placement for accurate measurements*
Pre-test microphone calibration is critical for accuracy

*In the canal microphone placement ensures the most accurate and representative measurement of the sound pressure level reaching the eardrum, directly accounting for the unique acoustic properties and resonances of an individual's ear canal and offering a degree of natural protection from the direct turbulent wind flow. Incorrect placement outside the ear canal can produce inaccurate wind noise reduction performance measurements.

Testing Environments:

Wind Tunnel: Our custom aeroacoustic open-walled wind tunnel ensures consistent and repeatable testing.
Real-World Testing: While less controlled, real-world testing on a bicycle provides valuable data under actual riding conditions. This involves riding at consistent speeds on a predefined course and recording wind noise.

Data Acquisition: The microphones capture the sound as an analog electrical signal, which is then converted into a digital signal using an Analog-to-Digital Converter. This digital data, representing the sound pressure fluctuations over time, is then ready for analysis. We use a Zoom audio recorder and TrueRTA, Sigview, and MATLAB for signal analysis.

Understanding Decibels: The Language of Sound Loudness
When we talk about sound levels, we use decibels. The decibel scale is fundamental to understanding wind noise.

Decibels (dB) are a logarithmic unit used to express the ratio of two values of a physical quantity, most commonly power or intensity. Because the human ear can perceive a vast range of sound pressures, a linear scale would be unwieldy; the logarithmic nature of the decibel scale allows for a more manageable and compressed representation. Specifically, the decibel scale is often used to measure sound intensity, where 0 dB is defined as the threshold of human hearing, and every increase of 10 dB represents a tenfold increase in sound intensity or power. This unit is not absolute but relative, making it highly useful for comparing sound levels, signal strengths, and other quantities that span a large range of magnitudes.

Decibels dB(A) is a weighted decibel measurement that specifically accounts for the sensitivity of the human ear. The A-weighting curve is a standard filter applied to sound pressure level measurements to better approximate how humans perceive loudness, particularly at different frequencies. The human ear is most sensitive to frequencies in the mid-range (around 1 kHz to 6 kHz) and is less sensitive to very low and very high frequencies. Therefore, a dB(A) measurement gives more emphasis to the frequencies the ear hears best and less to those it hears poorly, making it a more accurate representation of the perceived loudness of a sound compared to an unweighted decibel measurement (dB). This weighting is crucial in fields like environmental noise assessment, industrial safety, and hearing conservation, as it provides a single value that correlates well with the potential for hearing damage or annoyance.

Measuring and analyzing cycling ear wind noise involves a sophisticated approach that combines precise acoustic measurement with powerful signal processing techniques. By understanding the logarithmic nature of decibels, which quantify the loudness of the noise, and employing Fast Fourier Transform (FFT) to deconstruct its frequency components, researchers and product developers can gain invaluable insights into this ubiquitous cycling challenge. This detailed understanding is the foundation for developing innovative solutions that make cycling safer, more enjoyable, and ultimately, quieter.

This chart displays the frequency spectrum of wind noise, with two distinct lines showing the difference between unweighted decibel (dB) levels and A-weighted decibel (dBA) levels. The solid line (dB) represents the raw, unweighted sound pressure level across all frequencies. It shows a significant amount of sound energy concentrated in the very low-frequency range (below 100 Hz). The dashed line (dBA) applies an A-weighting filter, which mimics the way the human ear perceives loudness. Because the human ear is less sensitive to low-frequency sounds, the A-weighted curve is noticeably lower in this range. This visual comparison highlights that while a significant amount of sound energy exists at low frequencies (as shown by the dB line), much of it is not perceived as loud by the human ear.

Quantifying sound reduction, especially for turbulent airflow like cycling wind noise, is difficult using a simple linear percentage because sound is measured on a logarithmic decibel (dB) scale. Our perception of loudness is also non-linear and doesn't match a linear percentage scale. Accurately measuring noise reduction requires a multi-pronged approach that combines objective physical measurements with psychoacoustical models that capture the subjective human experience of hearing.

Here is a breakdown of different methods for calculating percentage reduction:

1. Percentage Reduction in Sound Pressure Level (SPL)

This method directly calculates the percentage reduction of the physical sound pressure measured by microphones.
Formula: Percentage Reduction$_{\text{SPL}} = (1 - 10^{(\Delta L / 20)}) \times 100%$. ΔL is the change in decibels (e.g., -20 dB).
Example: A 20 dB reduction results in a 90% reduction in sound pressure.

2. Percentage Reduction in Sound Intensity or Power

This method focuses on the reduction of acoustic power per unit area or total acoustic power.
Formula: Percentage Reduction$_{\text{Intensity/Power}} = (1 - 10^{(\Delta L / 10)}) \times 100%$. ΔL is the change in decibels (e.g., -20 dB).
Example: A 20 dB reduction results in a 99% reduction in sound intensity.

3. Percentage Reduction in Perceived Loudness (Psychoacoustical Approach)

This approach aligns with human perception, based on the principle that a 10 dB reduction roughly halves perceived loudness.
Formula:
- Loudness Ratio (x): x=2(∣ΔL∣/10).
- Percentage Reduction: Percentage Reduction$_{\text{Perceived Loudness}} = (1 - \frac{1}{x}) \times 100%$.
Example: A 20 dB reduction results in a 75% perceived loudness reduction.

4. Percentage Reduction for dB(A) Levels

This method applies the Perceived Loudness approach, to A-weighted decibel (dB(A)) values.
Cycling wind noise is predominantly low-frequency, and the A-weighting filter significantly reduces the contribution of these low frequencies, as human ears are less sensitive to them.
As a result, a smaller dB(A) reduction can still be a significant perceived reduction. For example, a 20 dBA reduction might yield a 75% perceived loudness reduction.