Typically with that type of cool season grass, the roots will be anywhere from 2-6". If the soil is primarily clay anticipate the roots to coincide with the shorter end of the spectrum. In addition, in compact soils, the roots will remain at a shorter depth because there are low levels of moisture and oxygen deeper in the soil.
Setting up an "as needed schedule" with the root depth of 2" is a great starting point. The roots are going to do most of their growing during the Spring, after which they won't experience much growth for the remainder of the year. That being said you won't have to worry about constantly switching depth levels as the year goes on.
Start with 2" and monitor the lawn during the Spring, if it looks healthy then it's safe to say you choose the right root depth, which should give you a healthy lawn all year. If you decide to switch depths then make the choice based off of your soil type, the rule of thumb being, denser soil, less root growth.