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Calculations and Limitations

Calculation of 10-day Obscuration

 The ten-day obscuration percentage (TDO) is basically a measure of the percentage of horizontal area which would be covered by dust during 10 days' exposure. It is therefore only meaningful when the samples to be assessed have been collected using a deposit gauge. Measuring samples collected in a flux gauge, for example the CERL gauge (BS1747 Pt5), will not therefore give a true indication of perceived dust nuisance. There is a popular misconception that these gauges measure dust deposition whereas in fact they attempt to measure dust flux. This flux is the vector product of airborne particle concentration (mass per unit volume) and the horizontal component of the windspeed (velocity) and thus has the units of mass per unit area per unit time. It is unfortunate that the units of dust flux are therefore the same as those of dust deposition, adding to the confusion. It is NOT possible to convert readings obtained by the directional gauge into deposition rates as the calculation would require knowledge of particle size, particle concentration and wind velocity components continuously during the sampling period, most of which are unlikely to be known; neither will adding the flux from the four collecting heads convert the results into units of deposition. In spite of the above comments, it is obviously possible to go through the motions of calculating TDO for a directional gauge (slot area 15300 mm²) but then it must be the user's responsibility to justify his figures.

The correct way of calculating TDO is to measure the entire sample in the absorptiometer, sum the results and calculate the TDO using this sum, the area of the deposit gauge aperture, area of absorptiometer sample beaker and the number of days for which the deposit gauge was exposed. However, it is possible to save time by using an aliquot sample, but great care must be taken to ensure that the sample chosen is truly representative.

 

Basic calculations are as shown below:

Effective Area of Absorptiometer Beaker = Ab mm²

Area of Dust Gauge Aperture = Ag mm²

Length of Exposure = D days

Sum of Absorptiometer Readings = T %

(Note that T may be greater than 100% as it is the sum of many values which can each be as great as 70%)

 

Then TDO = T * (Ab/Ag) * (10/D) % .. (1)

 

In the case of using an aliquot sample:

Effective Area of Absorptiometer Beaker = Ab mm²

Area of Dust Gauge Aperture = Ag mm²

Length of Exposure = D days

Single Absorptiometer Reading = S %

Volume of Aliquot Sample = Va ml

Total Sample Volume = Vt ml

 

Then TDO = S * (Ab/Ag) * (10/D) * (Vt/Va)% .. (2)

 

Examples:

Ab = 1963.5 mm²

Va = 94 ml (approximate volume in beaker with mask, filled to 100ml mark)

For a Hanby Frisbee Gauge, Ag = 40000 mm²

 

From (1) TDO = 0.49 * T/D % .. (3)

From (2) TDO = 0.49 * (S/D) * (Vt/94) %

ie TDO = 0.00522 * Vt * S/D % .. (4)

 

Figures for other gauges can be substituted in equations (1) or (2) as required.

 

Limitations

 Although the maximum theoretical hexagonal packing of dust particles in the absorptiometer beaker, assuming that they are approximately spherical, corresponds to an obscuration of 90%, the mathematical manipulation referred to in the operating principle limits the results to values between 0 and 70%, beyond which figure it is recommended that the sample be diluted as appropriate. The display will warn the user when this limit is reached. Because of the limitation of the microcontroller's analogue to digital converter to 10 bits, and the integer LCD display, the obscuration has an inbuilt tolerance of ± 1.

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