An airborne, tethered, multi-rotor wind turbine, effectively a rotorcraft kite, provides one platform for accessing the energy in high altitude winds. The craft is maintained at altitude by its rotors operating in autorotation, and its equilibrium attitude and dynamic performance are affected by the aerodynamic rotor forces, which in turn are affected by the orientation and motion of the craft. The aerodynamic performance of such rotors can vary significantly depending on orientation, influencing the efficiency of the system. This thesis analyzes the aerodynamic performance of an autorotating rotor through a range of angles of attack covering those experienced by a typical autogyro through that of a horizontal-axis wind turbine. To study the behavior of such rotors, an analytical model using the blade element theory coupled with momentum theory was developed. The model uses a rigid-rotor assumption and is nominally limited to cases of small induced inflow angle and constant induced velocity. The model allows for linear twist. In order to validate the model, several rotors -- off-the-shelf model-aircraft propellers -- were tested in a low speed wind tunnel. Custom built mounts allowed rotor angles of attack from 0 to 90 degrees in the test section, providing data for lift, drag, thrust, horizontal force, and angular velocity. Experimental results showed increasing thrust and angular velocity with rising pitch angles, whereas the in-plane horizontal force peaked and dropped after a certain value. The analytical results revealed a disagreement with the experimental trends, especially at high pitch angles. The discrepancy was attributed to the rotor operating in turbulent wake and vortex ring states at high pitch angles, where momentum theory has proven to be invalid. Also, aerodynamic design constants, which are not precisely known for the test propellers, have an underlying effect on the analytical model. The developments of the thesis suggest that a different analytical model may be needed for high rotor angles of attack. However, adding a term for resisting torque to the model gives analytical results that are similar to the experimental values.

The purpose of this honors thesis was to create a quadcopter equation of motion software model in order to develop a control system to make the quadcopter autonomous. This control system was developed using Matlab and Simulink, and the aspects of the quadcopter's flight that were chosen to be controlled were the roll angle, pitch angle, and height of the quadcopter. Upon the completion of this control system model, the actual quadcopter was to be constructed, flown, and used to collect experimental data for comparison to the model. However, the hardware was never made available due to back order problems, and so unfortunately no experimental data from actual test flights was able to be gathered and compared to the Simulink control system model. None the less, the final Simulink model is still accurate because the actual geometry of the chosen quadcopter was used during simulation (including the moments of inertia and moment arm lengths). To begin, background research into quadcopter design is presented to give insight into the progress that has been made in the design of this type of aircraft. The equations of motion for the quadcopter considered in the control system are then derived through the use of twelve state variables. The Simulink model for the open loop system was then constructed in a fashion that converts the change in rotor thrust to the associated orientation angles of the quadcopter. Linear approximations were then used to distinguish the open loop transfer functions for each controlled variable (roll angle, pitch angle, and height), and compensators were designed for the control system in order to produce a natural frequency and damping that allowed for a 5% settling time of approximately two seconds.

This study aims to showcase the results of a quadrotor model and the mathematical techniques used to arrive at the proposed design. Multicopters have made an explosive appearance in recent years by the controls engineering community because of their unique flight performance capabilities and potential for autonomy. The ultimate goal of this research is to design a robust control system that guides and tracks the quadrotor's trajectory, while responding to outside disturbances and obstacles that will realistically be encountered during flight. The first step is to accurately identify the physical system and attempt to replicate its behavior with a simulation that mimics the system's dynamics. This becomes quite a complex problem in itself because many realistic systems do not abide by simple, linear mathematical models, but rather nonlinear equations that are difficult to predict and are often numerically unstable. This paper explores the equations and assumptions used to create a model that attempts to match roll and pitch data collected from multiple test flights. This is done primarily in the frequency domain to match natural frequency locations, which can then be manipulated judiciously by altering certain parameters.

This thesis describes a longitudinal dynamic analysis of a large, twin-fuselage aircraft that is connected solely by the main wing with two tails unattached by a horizontal stabilizer. The goal of the analysis is to predict the aircraft’s behavior in various flight conditions. Starting with simple force diagrams of the longitudinal directions, six equations of motion are derived: three equations defining the left fuselage’s motion and three equations defining the right fuselage’s motion. The derivation uses a state-vector approach. Linearization of the system utilizes a Taylor series expansion about different trim points to analyze the aircraft for small disturbances about the equilibrium. The state transition matrix shows that there is a coupling effect from the reactionary moments caused by the two empennages through the connection of the main wing. By analyzing the system in multiple flight conditions: take-off, climb, cruise, and post-separation of payload, a general flight envelope can be developed which will give insight as to how the aircraft will behave and the overall controllability of the aircraft. The four flight conditions are tested with published Boeing 747 data confirmed from multiple sources. All four flight conditions contain unstable phugoid modes that imply instability increases with decreasing torsional spring stiffness of the wing or as the structural damping drops below 4%.

This thesis discusses the equilibrium conditions and static stability of a rotorcraft kite with a single main tether flying in steady wind conditions. A dynamic model with five degrees of freedom is derived using Lagrangian formulation, which explicitly avoids any constraint force in the equations of motion. The longitudinal static stability of the steady flight under constant wind conditions is analyzed analytically from the equilibrium conditions. The rotorcraft kite orientation and tether angle are correlated through the equation Γ=δ-ϑ, a necessary condition for equilibrium. A rotorcraft kite design with 3kg mass and 1.25m rotor radius is found to be longitudinally statically stable at 25,000ft with Γ>〖65〗^0 for wind speeds above 19m/s.