Worked example: BS 4142 rating level arithmetic

A BS 4142 rating level calculation has four quantities and one subtraction. Measure the background sound level, determine the specific sound level from the source, add any acoustic feature corrections to get the rating level, then subtract the background from the rating level. The excess is what the assessment turns on, and everything contentious in a BS 4142 report happens in the two steps before that subtraction.

The figures in the worked example below are illustrative and exist only to show the arithmetic.

The terms and what each one means

Four terms carry the method, and the standard uses them precisely.

The background sound level is the LA90 over the reference time interval: the level exceeded for 90 per cent of the period, representing the underlying quiet of the location without the source running.

The specific sound level is the LAeq of the source under assessment, at the assessment position, over the reference time interval.

The residual sound level is the ambient with the specific source removed. It matters when the specific sound has to be derived by subtraction rather than measured directly.

The rating level is the specific sound level plus acoustic feature corrections.

Reference time intervals are one hour during the day, taken as 07:00 to 23:00, and 15 minutes at night, 23:00 to 07:00. Using an hour at night, or a daytime 15 minute period, is a methodological error that an experienced reviewer will spot immediately.

Measuring the background

The background sound level is the measurement most often done badly, because it is the one that most affects the result and the one most exposed to judgement.

Measure at the assessment position, which is at the receptor rather than at the site boundary, and at a height representing the exposed facade. Measure over a period long enough to characterise the quiet times, which for a night-time assessment means several hours across more than one night.

Then choose the representative value. The standard does not prescribe an arithmetic mean, and taking the lowest single 15 minute LA90 of the week is as wrong as taking the average of everything. The usual approach is to identify the typical lowest levels during the period when the source will operate, exclude periods affected by extraneous events such as rainfall or a passing aircraft, and state clearly how the figure was chosen.

Record the weather. Wind speed and direction, rainfall and temperature all affect both measurement validity and propagation, and a reviewer will check them.

Determining the specific sound level

Three routes exist, in descending order of reliability.

Direct measurement at the receptor with the source operating and the residual sufficiently low. This is the cleanest and the least often available.

Measurement near the source, then calculation to the receptor using distance attenuation, directivity, screening and ground effects. This is the normal route for a proposed installation using manufacturer sound power data.

Derivation by subtracting the residual from the ambient. Valid, but the arithmetic becomes unstable when the specific sound is well below the residual, and the standard warns about it.

Whichever route is used, state the operating condition assessed. A condenser running at part load on a mild evening is not the design case, and the assessment should cover the worst realistic operating condition during the relevant period.

Acoustic feature corrections

Corrections are added to the specific sound level where the sound has a character that makes it more noticeable, and they are the part of the method most open to argument.

Tonality can be assessed subjectively or by the objective one-third octave band method set out in the standard. Use the objective method where the result is likely to be contested, and show the spectrum. A fan with a clear blade passing frequency, a transformer hum and a compressor whine all attract a correction.

Apply corrections once. Adding a tonal correction and an "other characteristics" correction for the same tonal quality is double counting, and it happens.

The worked example

Illustrative figures for a proposed external condenser serving a commercial unit, assessed at the nearest residential facade at night.

Under the standard, a difference of around 10 dB or more is an indication of a significant adverse impact, depending on context. A difference of around 5 dB is an indication of an adverse impact, again depending on context. Where the rating level does not exceed the background, that indicates a low impact.

Now mitigate. An attenuator and a change of unit reduce the specific sound level by 8 dB to 30 dB, and the acoustic treatment also removes the tonal character, so no correction applies. The rating level becomes 30 dB, two below the background. The same installation has moved from the upper band of the standard's indications to a low impact, and the only change is at the source.

That is the lesson of the arithmetic. Mitigation at source is worth more than any argument about the background figure.

Context and the limits of the comparison

The standard is explicit that the numerical difference is an indication rather than a verdict, and that context has to be considered.

Context means the absolute level as well as the difference. A rating level of 28 dB against a background of 20 dB is a 8 dB excess in a very quiet rural location, and the absolute level may still be below any level likely to disturb sleep. The reverse case, a small excess over a high urban background, may matter more than the number suggests because the character of the sound is different from the existing soundscape.

Context also covers the design of the receptor. A dwelling with mechanical ventilation and acoustically treated glazing, where windows do not need to be opened for cooling, is in a different position from one relying on open windows, and the standard expects that to be taken into account rather than assumed away.

State the uncertainty. Measurement uncertainty, the uncertainty in manufacturer data and the uncertainty in propagation modelling all belong in the report, and an assessment reporting a rating level to one decimal place without an uncertainty statement is overstating its own precision.

Reporting it so a reviewer can follow it

Set out the measurement positions on a plan, the instrumentation and calibration record, the survey dates, times and weather, the raw data, the chosen background value with the reasoning, the specific sound derivation, each correction with its justification, the rating level, the comparison and the context discussion.

A Noise Impact Assessment built that way can be checked line by line, which is what a reviewing acoustician or an environmental health officer wants. Councils expect a suitably qualified author, and professional review is strongly advised. Drafting support can carry the structure and the policy narrative, while the measurements, the corrections and the judgement belong to the practitioner. The professional directory is one route to a reviewer.

Every figure above is illustrative. Use the current version of the standard and the authority's own requirements.

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