Oscillatory or “Dutch Roll" Mode
The pair of complex roots of the characteristic equation for the lateral – directional motion of the Cherokee was given previously as -0.055±0.277i. When substituted into Equation 10.29 (using +0.277/) and Equation 10.30, the following results are obtained.
-0.192 + 0.864/
Replacing r by сгф gives
j|= -0.940 + 0.045/ or
j|= 0.941** (10.34)
where у = 177.3°.
Relating ф to <f>,
^7 = 1.06** (10.35)
where у = 74.8°.
This mode is a damped oscillation where the three angles ф, /3, and ф have approximately the same magnitudes. In the case of the Cherokee 180, the time to damp to half-amplitude equals 1.15 sec with a period of 2.07 sec.
The motion of the airplane for this mode can be described as follows. Imagine that the airplane begins to yaw to the right. As it does so, it slips to
the left, so that its path remains nearly a straight line. As it yaws to the right, it begins to roll in that direction. While still rolled to the right, the airplane begins to yaw to the left and slip to the right. This turning and rolling motion is somewhat mindful of the weaving and twisting that an ice skater undergoes in skating along the ice. Hence the mode has come to be called the “Dutch roll” after the country well known for its ice skating.
This mode, for the Cherokee 180, is barely discernable to the pilot. It can be excited by a step input to the rudder and is observable. However, as predicted, it damps rapidly. For some airplanes the Dutch roll mode is lightly damped, making them somewhat unpleasant to fly. One gets the feeling that the rear end is trying to pass the front end.