## Description

Calculates time constants at each point through the entire profile for the temperature sensor on dropsondes using the pressure, temperature, and fall rate at that point. The fall rate used can be either the theoretical fall rate or the observed fall rate.

## Formula

$$TC(pres, tdry, dz)$$, where $$tdry$$ is in degrees Kelvin, is calculated as:

$$TC = \frac{heatCapacity} {hCoef \times area} \\$$ where: $$hCoef = \frac{Nu \times k} {diameter}\\ k = \frac{6.325 \times 10^{-7} tdry^{1.5}} {tdry + 245.4 \times 10^{\frac{12}{tdry}}}\\ Nu = 0.37Re^{0.6}\\ Re = \frac{density \times abs(dz) \times diameter} {viscosity}\\ density = \frac{pres \times 100}{tdry \times 287}\\ viscosity = \frac{1.458 \times 10^{-6} tdry^{1.5}}{tdry + 110.4}$$

### Constants

The values of the following constants depend upon the sensor type:

 Constant RS80 RS90/92 $$heatCapacity$$ $$2.6 \times 10^{-6}$$ $$8.5532 \times 10^{-8}$$ $$area$$ $$0.000014$$ $$6.3 \times 10^{-7}$$ $$diameter$$ $$0.00215$$ $$0.00013$$

### RS41 sensor

Rather than change the constants for the RS41 sensor, the resulting time constant is divided by 4.

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