# What is the difference between rate of roll and roll displacement?

I was studying Principles of Flight, I came across a sentence which is my question.

_ the aileron is known as a rate control since a given aileron angle of deflection determines a rate of roll, not a roll displacement.

My 1st question is what is the difference between rate of roll and roll displacement? What is roll displacement?

My 2nd question is, I know rate of roll is the rate at which an aircraft executes a turn expressed in degrees per second, can we say that rate of roll is the rate of change of heading as the aircraft rolls about its longitudinal axis?

• Your "2nd question" conflates roll rate with turn rate; heading change is turn rate; bank angle change is roll rate. In the case of an aileron roll, you could have a high roll rate with essentially zero heading change or turn rate; in a turn with a constant bank angle, you'd have zero roll rate with a constant turn rate.
– Ralph J
Apr 9 at 13:11

Roll displacement is basically the bank angle of the aircraft. Rate of roll is the rate of change of bank angle per unit time: $$\large \frac {∆bank \ angle}{∆time}$$