### Dynamic Response » Response to Specific Input Functions » Ramp Function

The “ramp” variation in the measurand occurs when the measurand increases at a constant rate, as shown by the red line in the figure.

First and second order response to a measurand changing at a constant rate (ramp). Image from NCAR/EOL.

The sensor output in both cases, after a transient period, follows the slope of the measurand but with a delay. For the first-order case, the effective delay, also known as the dynamic lag, is equal to the time constant so this is often a useful way to determine that time constant. In the case of aircraft-borne temperature sensors, this response will result in a difference between aircraft ascent and descent profiles, and the time constant of the sensors can be determined from that difference.

For a second-order sensor, the delay is 2𝛄 / ω and, for the parameters shown, is larger than the first-order delay 𝜏 .

A sounding with a lag of 2 s with a climb rate of 20 m/s and a temperature gradient of 10°C per km should produce a difference of about 0.8°C between climb (blue curve) and descent (red curve). While this diagram shows the expected difference, there is almost always enough real variability in the atmosphere to mask an effect. Image from NCAR/EOL.