Measurement uncertainty: what a wet-bulb reading costs the result

Quadrature against naive addition of the reading uncertainties, and each reading's share.

Combined standard uncertainty against the uncertainty of the wet-bulb reading, with quadrature addition σ = √(σcw² + σwb²) against the naive sum — and the share of the total variance each reading contributes.

Reference conditions: cold-water reading ±0.20 K, wet-bulb reading ±0.50 K — 0.54 K by quadrature against 0.70 K by naive addition, with the wet bulb supplying 86 % of the variance.

Formula: σ = √(σcw² + σwb²), with the variance share σwb² / σ².

Measurement uncertainty chart: combined uncertainty against the wet-bulb reading's uncertainty, comparing quadrature addition (0.54 K at ±0.5 K) with the naive sum (0.70 K), with the wet bulb supplying about 86 % of the total variance (illustrative)Illustrative uncertainty chart for a cooling-tower performance test, following the post's two rules. The lower curve is quadrature addition, σ = √(σcw² + σwb²), with the cold-water reading fixed at ±0.20 K and the wet-bulb reading varying from 0 to 0.6 K along the x axis; the upper straight line is the naive sum σcw + σwb. The hatched band between them is the overstatement naive addition produces — 0.54 K against 0.70 K at the wet bulb of ±0.50 K, or 0.16 K (30 %) too much; at ±0.2 K the two rules agree at 0.28 K against 0.40 K, and at 0.6 K quadrature gives 0.63 K against 0.80 K. The wet bulb supplies 86 % of the total variance at the post's example (0.25 of 0.29 K squared: variances add, so the share of the total is a variance share), so the wet-bulb sensor sets the floor for the whole result. Values are computed from the formulas, not measured. (chart-uncertainty)Uncertainty — Illustrative — not a measurementQuadrature vs naive addition0.00.10.20.30.40.50.60.00.20.40.60.81.0Wet-bulb uncertainty σwb (K)Combined uncertainty (K)0.540.70naive sumquadratureReference: cold-water reading ±0.20 K · wet bulb ±0.50 Kσ = √(σcw² + σwb²) — independent errors add in quadratureσ cold water (K)±0.20σ wet bulb (K)±0.50quadrature √(0.20² + 0.50²) (K)0.54naive 0.20 + 0.50 (K)0.70naive overstates by+0.16 K (+30 %)wet-bulb variance share86 %Computed from the formula — not field data.
Illustrative, computed from the two rules above — not a measurement. The lower curve is quadrature addition, the straight line the naive sum, and the band between them is the uncertainty that naive addition overstates.

Sources