Definition
The time required for a quantity changing exponentially toward a final value to reach approximately 63.2 percent of the total change. It is a measure of how quickly a system, such as a capacitor charging through a resistor or a gyro spinning up, responds to a change in input.
Plain English
A number that tells you how fast something settles to a new value. After one time constant, the change is about two-thirds of the way complete.
Context Anchor
Seen in discussions of aircraft instruments, sensors, temperature indications, pressure instruments, and other systems that do not respond instantly.
Derivation
From Latin 'constans' meaning 'standing firm' or 'unchanging.' The value is called a constant because, for a given system, it is a fixed property -- the same circuit or instrument always responds at the same rate.
Why Pilots Care
Instruments and electrical systems do not respond instantly. Knowing an instrument has a noticeable time constant explains why a vertical speed indicator or turn coordinator lags behind the actual aircraft motion for a moment after a control input.
Analogy
Like filling a sink where the drain partly resists the water -- the level rises quickly at first, then more slowly as it approaches full. The time constant is how long it takes to get most of the way there.
Grounding Statement
When the real condition changes suddenly, the indicated value may move gradually, and the time constant describes that delay.
Intuition Check
Do not read constant as meaning the reading never changes. Here, constant means a fixed response-time value used to measure how quickly the reading changes.
Example Sentence 1
The instrument's short time constant means it responds quickly to small changes in pitot pressure.
Example Sentence 2
A shorter time constant in the heading hold mode lets the autopilot correct deviations more quickly.