Methodology

Noise Pollution #

Noise is a byproduct of useful energy use in a system. In our model we assume that the main source of noise is the cooling systems which dissipate the heat produced by the servers.

Calculation #

Energy Usage

The energy used by cooling systems can be estimated using the total facility power (P_total) and the Power Usage Effectiveness (PUE) — the ratio of total facility power to the power used by the IT equipment. The cooling power Q_cool is then:

Q_{\text{cool}} = P_{\text{total}} \times \frac{\text{PUE} - 1}{\text{PUE}}

For example: a data center with 130 MW total power and a PUE of 1.3 uses approximately 30 MW for cooling.

Sound Power Level

The sound produced by a cooling system is estimated by the following approximation [1], where L_w is the sound power level in dB and A is an empirical constant that varies by equipment type:

L_w = A + 10 \times \log_{10}(Q_{\text{cool}})

We use the following values for A, which fall within reasonable estimates of modern cooling systems:

Air-cooled: A = 87 dB
Liquid-cooled: A = 84 dB

Noise Propagation

A point source propagation formula [2] gives the radius r at which noise falls to a target level L_p,target:

r = 10^{\left(\frac{L_w - 11 - L_{p,\,\text{target}}}{20}\right)} \; \text{metres}

Assumptions #

Assumes a point source at the midpoint of the data center. Does not account for multiple buildings and their arrangement.
Does not take into account environmental blocking or reflection from buildings.
Details on PUE, total power and type of cooler are not known for all data centers and so this represents a conservative estimate given all available knowledge.

References #

[1] ASHRAE. ASHRAE Handbook — HVAC Applications. Atlanta, GA: American Society of Heating, Refrigerating and Air-Conditioning Engineers. (Chapter 48: Noise and Vibration Control.)
[2] ISO 9613-2:1996. Acoustics — Attenuation of sound during propagation outdoors — Part 2: General method of calculation (§7.3.1).