  In this report, we present the theory on aerodynamics of quadrotors using the
well established momentum and blade element theories. From a robotics
perspective, the theoretical development of the models for thrust and
horizontal forces and torque (therefore power) are carried out in the body
fixed frame of the quadrotor. Using momentum theory, we propose and model the
existence of a horizontal force along with its associated power. Given the
limitations associated with momentum theory and the inadequacy of the theory to
account for the different powers represented in a proposed bond graph lead to
the use of blade element theory. Using this theory, models are then developed
for the different quadrotor rotor geometries and aerodynamic properties
including the optimum hovering rotor used on the majority of quadrotors. Though
this rotor is proven to be the most optimum rotor, we show that geometric
variations are necessary for manufacturing of the blades. The geometric
variations are also dictated by a desired thrust to horizontal force ratio
which is based on the available motor torque (hence power) and desired flight
envelope of the vehicle. The detailed aerodynamic models obtained using blade
element theory for different geometric configurations and aerodynamic
properties of the aerofoil sections are then converted to lumped parameter
models that can be used for robotic applications. These applications include
but not limited to body fixed frame velocity estimation and individual rotor
thrust regulation [1, 2].
