When the input to a sensor is changing rapidly, we observe performance characteristics that are due to the change in input and are not related to static performance characteristics. In this chapter we will assume that a static calibration has been applied so that we can consider dynamic performance independently of static characteristics. The terms “linear” and “nonlinear” have been used in chap. 3 in the static sense. Now they are being used in the dynamic sense where “linear” connotes the applicability of the superposition property. A given sensor could be nonlinear in the static sense (e.g., a PRT is nonlinear in that is static sensitivity is not constant over the range) but could be linear in the dynamic sense (modeled by a linear differential equation). We use differential equations to model this dynamic performance while realizing the models can never be exact. If the dynamic behavior of physical systems can be described by linear differential equations with constant coefficients, the analysis is relatively easy because the solutions are well known. Such equations are always approximations to the actual performance of physical systems that are often nonlinear, vary with time, and have distributed parameters. The justification for the use of simple, readily solved models must be the quality of the fit of the solution to the actual system output and the usefulness of the resulting analysis. Dynamic performance characteristics define the way instruments react to measurand fluctuations. When a temperature sensor is mounted on an airplane these characteristics will indicate what the sensor “sees.” If the airplane flies through a cloud with a slow sensor (where time constant is large) it may not register change of temperature or humidity. That would not be tolerable if we wanted to measure the cloud. Similarly, if the airplane flies through turbulence we would like to measure changes in air speed. Variations in temperature and humidity would be vital in the flight of a radiosonde, so again the time constant of the sensors would be considered. Fluxes of heat, water vapor, and momentum near the ground require fast sensors (with small time constants).
Torsional pendulum with small time constant