What is roll mode time constant and why is it important?

Roll mode is a first-order response characterized by time constant tau_r = -1/Lp where Lp is roll damping derivative. After a step aileron input, roll rate builds up exponentially: p = p_steady * (1 - e^(-t/tau_r)). Smaller time constant means faster roll response. Handling qualities requirements (MIL-STD-1797) specify maximum tau_r typically 1.0-1.4 seconds for Category A flight phases, with tighter limits for fighters. Roll time constant depends on: wing span (larger wings, larger tau_r), altitude (decreases with dynamic pressure), and roll damping derivative. Fast roll response is essential for combat aircraft and crosswind landing.