Table 2.2: Experimentally determined aircraft inertias [kg-m21 Aircraft Roll Axis I Pitch Axis Yaw Axis N 0.46 0.65 0.61 0.63 Mean 0.30 0.42 0.63 Std Dev.I 0.029 0.011 0.021 Using the small angle approximation for a since L R, and substituting known values from Eqs. 2.1 and 2.2, Eq 2.3 reduces to Irao L which is characterized by the undamped natural frequency, w, and period of oscilla Tp R2 (2.5) 2 By finding averaged values for the period of oscillation, Tp, in each of the pitch, roll and yaw axes, the inertia about each axis can be approximated. This experiment neglects aerodynamic and other forms of damping as well as the cross-axis inertias (e. g,, Ixz, Iy2). The experimental results are summarized for each of the axes and three different aircraft in the same configuration in Table 2.2, showing agreement between different vehicles used in the tests. The largest variation was found in the roll axis due to the difficulty of mounting the aircraft through the center of gravity, which is essential in this experimental setup 2.1.2 Actuator Models The servos used on the aircraft have saturation limits. limited bandwidth and limited slew rates which are captured in the actuation models of the Cloud Cap hardware-� Table 2.2: Experimentally determined aircraft inertias [kg­m2] Aircraft Roll Axis Pitch Axis Yaw Axis No. Ixx Iyy Izz 1 0.28 2 0.30 3 0.33 Mean 0.30 Std Dev. 0.029 0.46 0.44 0.47 0.42 0.011 0.65 0.61 0.63 0.63 0.021 Using the small angle approximation for α since L � R, and substituting known values from Eqs. 2.1 and 2.2, Eq. 2.3 reduces to ¨ mgR2 Ixxφ + φ = 0 (2.4) L which is characterized by the undamped natural frequency, ω, and period of oscilla￾tion, Tp ω = mgR2 IxxL (2.5) 2π Tp = ω (2.6) By finding averaged values for the period of oscillation, Tp, in each of the pitch, roll, and yaw axes, the inertia about each axis can be approximated. This experiment neglects aerodynamic and other forms of damping as well as the cross­axis inertias (e.g., Ixz, Iyz). The experimental results are summarized for each of the axes and three different aircraft in the same configuration in Table 2.2, showing agreement between different vehicles used in the tests. The largest variation was found in the roll axis due to the difficulty of mounting the aircraft through the center of gravity, which is essential in this experimental setup. 2.1.2 Actuator Models The servos used on the aircraft have saturation limits, limited bandwidth, and limited slew rates which are captured in the actuation models of the Cloud Cap hardware­ 35